We study weighted energy efficiency maximization for multiple-input multiple-output cognitive multiple access channels under both secondary user transmit power constraint and primary user interference power constraint. Energy efficiency is defined as the ratio of weighted sum rate and energy consumption including both transmission and circuit energy consumption. The nonlinear (fractional programming) energy efficiency optimization problem is transformed into a series of parametrized convex optimization problems. A combination of bisection search method and cyclic coordinate ascent-based iterative water-filling algorithm is proposed to solve the parametrized problem. Computer simulation examples are provided to illustrate the proposed approach and to explore the trade-off between energy efficiency and spectrum efficiency.