diff --git a/src/common/error/src/status_code.rs b/src/common/error/src/status_code.rs
index baf366ae9f..747514ba44 100644
--- a/src/common/error/src/status_code.rs
+++ b/src/common/error/src/status_code.rs
@@ -83,10 +83,12 @@ pub enum StatusCode {
 }
 
 impl StatusCode {
+    /// Returns `true` if `code` is success.
     pub fn is_success(code: u32) -> bool {
         Self::Success as u32 == code
     }
 
+    /// Returns `true` if the error with this code is retryable.
     pub fn is_retryable(&self) -> bool {
         match self {
             StatusCode::StorageUnavailable
@@ -114,6 +116,35 @@ impl StatusCode {
             | StatusCode::AccessDenied => false,
         }
     }
+
+    /// Returns `true` if we should print an error log for an error with
+    /// this status code.
+    pub fn should_log_error(&self) -> bool {
+        match self {
+            StatusCode::Unknown
+            | StatusCode::Unsupported
+            | StatusCode::Unexpected
+            | StatusCode::Internal
+            | StatusCode::PlanQuery
+            | StatusCode::EngineExecuteQuery
+            | StatusCode::StorageUnavailable
+            | StatusCode::RuntimeResourcesExhausted => true,
+            StatusCode::Success
+            | StatusCode::InvalidArguments
+            | StatusCode::InvalidSyntax
+            | StatusCode::TableAlreadyExists
+            | StatusCode::TableNotFound
+            | StatusCode::TableColumnNotFound
+            | StatusCode::TableColumnExists
+            | StatusCode::DatabaseNotFound
+            | StatusCode::UserNotFound
+            | StatusCode::UnsupportedPasswordType
+            | StatusCode::UserPasswordMismatch
+            | StatusCode::AuthHeaderNotFound
+            | StatusCode::InvalidAuthHeader
+            | StatusCode::AccessDenied => false,
+        }
+    }
 }
 
 impl fmt::Display for StatusCode {
diff --git a/src/servers/src/grpc/handler.rs b/src/servers/src/grpc/handler.rs
index f28ef70e87..aa4c6f8a16 100644
--- a/src/servers/src/grpc/handler.rs
+++ b/src/servers/src/grpc/handler.rs
@@ -19,7 +19,7 @@ use api::v1::{Basic, GreptimeRequest, RequestHeader};
 use common_error::prelude::ErrorExt;
 use common_query::Output;
 use common_runtime::Runtime;
-use common_telemetry::timer;
+use common_telemetry::{logging, timer};
 use metrics::increment_counter;
 use session::context::{QueryContext, QueryContextRef};
 use snafu::OptionExt;
@@ -73,11 +73,22 @@ impl GreptimeRequestHandler {
         //   - Obtaining a `JoinHandle` to get the panic message (if there's any).
         //     From its docs, `JoinHandle` is cancel safe. The task keeps running even it's handle been dropped.
         // 2. avoid the handler blocks the gRPC runtime incidentally.
-        let handle = self
-            .runtime
-            .spawn(async move { handler.do_query(query, query_ctx).await });
+        let handle = self.runtime.spawn(async move {
+            handler.do_query(query, query_ctx).await.map_err(|e| {
+                if e.status_code().should_log_error() {
+                    logging::error!(e; "Failed to handle request");
+                } else {
+                    // Currently, we still print a debug log.
+                    logging::debug!("Failed to handle request, err: {}", e);
+                }
+                e
+            })
+        });
 
         let output = handle.await.map_err(|e| {
+            // logs the runtime join error.
+            logging::error!("Failed to join handle, err: {}", e);
+
             if e.is_cancelled() {
                 Status::cancelled(e.to_string())
             } else if e.is_panic() {