Native American Psychiatric and Mental Health Care Improvement Act - Directs the Secretary of Health and Human Services (HHS) to award a five-year grant to one department of psychiatry in, or one non-profit entity affiliated with, an accredited medical school in this country to carry out a demonstration program to recruit, train, deploy, and professionally support psychiatric physicians who agree to provide primary and specialty health care services in Indian health programs for at least two years.

Requires the grantee to: (1) create a nationally-replicable workforce model that identifies and incorporates best practices for carrying out such activities, and (2) provide participating psychiatric physicians with up to one year of supplemental clinical and cultural competency training that enables them to provide primary and specialty health care services in Indian health programs.

Requires participating psychiatric physicians to: (1) be licensed or eligible for licensure to practice in the state to which they will be deployed; and (2) demonstrate a commitment, beyond the one year of training and two years of deployment, to a career as a specialty care or primary care physician providing mental health services in Indian health programs. Gives a preference to psychiatric physicians who are American Indians or Alaska Natives.

Directs the Secretary to make a repayment, under the Indian Health Service Loan Repayment Program, of the educational loans of participating psychiatric physicians for each year of their deployment to an Indian health program.