Military Judicial Reform Act of 2013 - Amends the Uniform Code of Military Justice (UCMJ) to require a convening authority (the person taking action on the findings of a court-martial), as soon as practicable after receipt of the findings and sentence of a court-martial, to approve the sentence in whole. Prohibits such authority from modifying such findings or sentence. (Under current law, modifying findings or a sentence is a command prerogative involving the sole discretion of such authority.) Allows certain other officials to act in place of the convening authority.

Allows the accused in a court-martial to submit to the convening authority matters for inclusion in the final record of trial. (Under current law, such accused may submit matters for consideration with respect to the findings and sentence.) Removes the requirement that a convening authority obtain and consider the recommendation of his/her staff judge advocate or legal officer.

Repeals the authority of a convening authority to suspend the execution of any sentence or part thereof other than a death sentence.