We present a transmit power adaptive filter-bank multicarrier with offset quadrature amplitude modulation (FBMC-OQAM) waveform for joint communication and radar system. For frequency selective fading channels or frequency sensitive targets, a joint optimization problem is designed by taking both the radar detection performance and communication channel capacity into the objective function under the constraint of limited transmit power. In addition, we derive the power allocation condition where the optimal performance of radar and communication can be achieved simultaneously. Otherwise, the tradeoff between radar and communication performance is necessary by adjusting the weighting factor. The proposed algorithm can realize adaptive transmission where the parameters of the transmitting waveform can be optimally designed for the next pulse by utilizing the measured values of the current signal and the channel state information. Moreover, the feasibility and advantages of FBMC as the radar signal are analyzed from the aspects of average ambiguity function, multipath effect and Doppler shift. Simulation results verify the effectiveness of the proposed scheme. Compared with the equal power allocation, the proposed adaptive transmission power algorithm in this paper shows better performance.