This letter investigates a robust transmit beamforming design for a dual-function radar-communication (RadCom) system in the presence of direction mismatch. We simultaneously consider the desired beampattern of the radar function of the radar target and the signal-to-interference-plus-noise ratios (SINRs) of the multi-user communication as the performance metric. A properly-weighted scheme is proposed to optimize the related figure of merits under the transmit power and the powers of the direction mismatch spatial ranges of interference constraints, which is nonconvex due to the fractional framework and the transmit power constraints. To tackle this issue, we derive an iterative procedure with Dinkelbach’s framework based on a sequential optimization procedure (Dinkelbach-SOP), and the minorization-maximization framework under the alternating direction method of multipliers (MM-ADMM). Finally, we demonstrate numerically that the proposed design provides effectiveness.