A hybrid overlay/underlay spectrum sharing method for cognitive radio networks based on user classification and convex optimization is proposed. Interference radii are configured for the primary receiver and each cognitive receiver. Cognitive users are divided into four groups and allocated different spectrum sharing patterns according to their distance from the primary transmitter and receiver. An optimal power allocation scheme that achieves the maximum sum rate of cognitive radio system on the premise of satisfying the interference constraint of primary receiver is acquired through the convex optimization method. Performance analysis and simulation results show that, compared with existing methods, our method leads to improved performance of achievable sum rate of cognitive users while guarantees the transmission of primary users.