diff --git a/crates/oxc_linter/src/context/host.rs b/crates/oxc_linter/src/context/host.rs
index f9770f5c79df5..f204aa9063c16 100644
--- a/crates/oxc_linter/src/context/host.rs
+++ b/crates/oxc_linter/src/context/host.rs
@@ -194,6 +194,11 @@ impl<'a> ContextHost<'a> {
         &mut self.sub_hosts[self.current_sub_host_index.get()]
     }
 
+    // Whether the current sub host is the first one.
+    pub fn is_first_sub_host(&self) -> bool {
+        self.current_sub_host_index.get() == 0
+    }
+
     /// Shared reference to the [`Semantic`] analysis of current script block.
     #[inline]
     pub fn semantic(&self) -> &Semantic<'a> {
diff --git a/crates/oxc_linter/src/rules/unicorn/filename_case.rs b/crates/oxc_linter/src/rules/unicorn/filename_case.rs
index 26aa9517687bc..b3297d8c42394 100644
--- a/crates/oxc_linter/src/rules/unicorn/filename_case.rs
+++ b/crates/oxc_linter/src/rules/unicorn/filename_case.rs
@@ -6,7 +6,10 @@ use oxc_macros::declare_oxc_lint;
 use oxc_span::Span;
 use serde_json::Value;
 
-use crate::{context::LintContext, rule::Rule};
+use crate::{
+    context::{ContextHost, LintContext},
+    rule::Rule,
+};
 
 fn filename_case_diagnostic(message: String, help_message: String) -> OxcDiagnostic {
     OxcDiagnostic::warn(message).with_label(Span::default()).with_help(help_message)
@@ -258,6 +261,10 @@ impl Rule for FilenameCase {
 
         ctx.diagnostic(filename_case_diagnostic(message, help_message));
     }
+
+    fn should_run(&self, ctx: &ContextHost<'_>) -> bool {
+        ctx.is_first_sub_host()
+    }
 }
 
 #[test]
@@ -441,6 +448,8 @@ fn test() {
             serde_json::json!([{ "case": "snakeCase", "multipleFileExtensions": false }]),
         ),
         ("", None, None, Some(PathBuf::from("FooBar.tsx"))),
+        // should only report once
+        ("<script></script><script setup></script>", None, None, Some(PathBuf::from("FooBar.vue"))),
     ];
 
     Tester::new(FilenameCase::NAME, FilenameCase::PLUGIN, pass, fail).test_and_snapshot();
diff --git a/crates/oxc_linter/src/snapshots/unicorn_filename_case.snap b/crates/oxc_linter/src/snapshots/unicorn_filename_case.snap
index 3aec1b0c8876e..2905b77fa480b 100644
--- a/crates/oxc_linter/src/snapshots/unicorn_filename_case.snap
+++ b/crates/oxc_linter/src/snapshots/unicorn_filename_case.snap
@@ -160,3 +160,10 @@ source: crates/oxc_linter/src/tester.rs
    ╭─[filename_case.tsx:1:1]
    ╰────
   help: Rename the file to 'foo-bar.tsx'
+
+  ⚠ eslint-plugin-unicorn(filename-case): Filename should be in kebab case
+   ╭─[filename_case.tsx:1:9]
+ 1 │ <script></script><script setup></script>
+   ·         ▲
+   ╰────
+  help: Rename the file to 'foo-bar.vue'