Comprehensive Immunosuppressive Drug Coverage for Kidney Transplant Patients Act of 2013 - Amends title II (Old Age, Survivors and Disability Benefits) (OASDI) of the Social Security Act (SSA) to extend the months of coverage of immunosuppressive drugs for kidney transplant patients.

Amends SSA title XVIII (Medicare) to make eligible for enrollment in Medicare part B (Supplementary Medical Insurance), solely for the purpose of such drug coverage, every individual whose insurance benefits under Medicare part A (Hospital Insurance) have ended by reason of a kidney transplant or the end of any requirement for a regular course of dialysis.

Directs the Secretary of Health and Human Services (HHS) to determine a monthly premium rate for such individuals equal to 35% of the monthly actuarial rate for enrollees age 65 and over. Prescribes a formula for detemination of a government contribution to such a premium.