Multiple-input multiple-output (MIMO) has been used in wireless communications to increase data rates via multiplexing or improve performance via diversity. Additionally, in radar systems, MIMO promises improved parameter identifiability and target resolution. Frequency diverse (FD)-MIMO radar can effectively distinguish targets that are closely spaced in the same angle cell by exploiting its range-angle-dependent transmit beamform. Therefore, in this paper, we first propose an integrated waveform design by embedding weighted, phase-modulated communication signals in the FD-MIMO radar waveform. Then, we derive the Cramer-Rao lower bound (CRLB) of the location estimation and analyze the communication performance achieved when the communication receiver extracts information from the integrated signals. Next, transmit beamforming is optimized to achieve the best tradeoff between the radar and communication performances of the system. Due to the nonconvexity of the optimization problem, we apply sequential parametric convex approximation (SPCA) and semidefinite relaxation (SDR) methods to solve the problem. The simulation results reveal the effects of some parameters, such as the frequency interval, symbol period, and communication symbol sequence, on radar and communication performance and demonstrate the tradeoff between radar and communication obtained by optimizing the transmit beamforming vector.