diff --git a/concore_cli/commands/init.py b/concore_cli/commands/init.py
index 53fd53f..cfaf73c 100644
--- a/concore_cli/commands/init.py
+++ b/concore_cli/commands/init.py
@@ -258,8 +258,14 @@ def _build_graphml(project_name, selected_langs):
 # ---------------------------------------------------------------------------
 
 
+def _check_project_name(name):
+    if name in (".", "..") or Path(name).name != name:
+        raise ValueError("Project name must not contain path separators")
+
+
 def init_project_interactive(name, selected_langs, console):
     """Create a project with one node per selected language (no edges)."""
+    _check_project_name(name)
     project_path = Path(name)
 
     if project_path.exists():
@@ -327,6 +333,7 @@ def init_project_interactive(name, selected_langs, console):
 
 def init_project(name, template, console):
     """Non-interactive init — single Python node skeleton."""
+    _check_project_name(name)
     project_path = Path(name)
 
     if project_path.exists():
diff --git a/tests/test_cli.py b/tests/test_cli.py
index d746040..e6d7ab2 100644
--- a/tests/test_cli.py
+++ b/tests/test_cli.py
@@ -2,12 +2,15 @@
 import tempfile
 import shutil
 import os
+import sys
 import json
 from pathlib import Path
 from unittest.mock import patch
 from click.testing import CliRunner
 from concore_cli.cli import cli
 
+cli_module = sys.modules[cli.callback.__module__]
+
 
 class TestConcoreCLI(unittest.TestCase):
     def setUp(self):
@@ -55,6 +58,19 @@ def test_init_existing_directory(self):
             self.assertNotEqual(result.exit_code, 0)
             self.assertIn("already exists", result.output)
 
+    def test_init_rejects_path_like_name(self):
+        # init must not create the project outside the current directory (#588)
+        for args in (["init", "../x"], ["init", "../x", "--interactive"]):
+            with self.subTest(args=args):
+                with self.runner.isolated_filesystem(temp_dir=self.temp_dir):
+                    with patch.object(
+                        cli_module, "run_wizard", return_value=["python"]
+                    ):
+                        result = self.runner.invoke(cli, args)
+                    self.assertNotEqual(result.exit_code, 0)
+                    self.assertIn("path separators", result.output)
+                    self.assertFalse(Path("../x").exists())
+
     def test_validate_missing_file(self):
         result = self.runner.invoke(cli, ["validate", "nonexistent.graphml"])
         self.assertNotEqual(result.exit_code, 0)