diff --git a/docs/.linkcheckerrc b/docs/.linkcheckerrc
index 40aa898c0e26..e6ab4ea1a5df 100644
--- a/docs/.linkcheckerrc
+++ b/docs/.linkcheckerrc
@@ -9,6 +9,7 @@ threads=1
 ignore=
   pythonapi/lightgbm\..*\.html.*
   http.*amd.com/.*
+  https.*tandfonline.com/.*
 ignorewarnings=http-robots-denied,https-certificate-error
 checkextern=1
 
diff --git a/docs/Parallel-Learning-Guide.rst b/docs/Parallel-Learning-Guide.rst
index ec75eac640a1..f30f4c0b1e22 100644
--- a/docs/Parallel-Learning-Guide.rst
+++ b/docs/Parallel-Learning-Guide.rst
@@ -544,6 +544,6 @@ See `the mars documentation`_ for usage examples.
 
 .. _the lightgbm_ray documentation: https://docs.ray.io/en/latest/tune/api_docs/integration.html#lightgbm-tune-integration-lightgbm
 
-.. _Mars: https://docs.pymars.org/en/latest/index.html
+.. _Mars: https://mars-project.readthedocs.io/en/latest/
 
-.. _the mars documentation: https://docs.pymars.org/en/latest/user_guide/learn/lightgbm.html
+.. _the mars documentation: https://mars-project.readthedocs.io/en/latest/user_guide/learn/lightgbm.html