1) Google the name of the journal to get to the publisher's webpage.
Look for a section on the page "about this journal".
If it is a peer-reviewed publication, it will proudly advertise itself as such.
2) There is also a library database that supplies this information. It is called, "Ulrich's".
It is listed on the library's webpage > click: Subject Databases > A-Z Databases > "U" tab >
scroll down list to find "Ulrich's".
**Something to think about: A journal can be peer-reviewed and still contain individual articles that are NOT peer-reviewed...for example, editorials and book reviews are pieces that are not peer-reviewed.