A similar proposal last year didn't make it out of the state Legislature.
Martinez made the latest request Monday while visiting the Albuquerque Veterans' Memorial.
Military retirees currently living in New Mexico are fully taxed on their pension income.
The governor's office says 25 other states currently offer some sort of military retiree pension income tax exemption.
Martinez says retirees who start second careers or businesses using highly technical skills obtained in the military often look past New Mexico when they return to civilian life.
She says demand is increasing for veterans trained in aviation, technology and engineering.