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Due to the flourishing development of vehicle-to-vehicle (V2V) communications and autonomous driving, interference between radar sensing and communication signals becomes a challenging issue. We propose a transmit beamforming based spectrum sharing scheme to achieve peaceful coexistence between automotive multiple-input multiple-out (MIMO) radar and communication systems. Our objective is to maximize the signal-to-interference-plus-noise ratio (SINR) of the automotive radar receiver subject to the communication capacity and the transmitted power budget constraints to optimize both the communication covariance matrix and the radar transmit precoder. The formulated optimization problem is non-convex, which is converted to convex by introducing a new slack variable and then solving it using the block coordinate descent, also called alternation optimization, approach. Additionally, the ellipsoid sub-gradient method is then employed to reduce the computational complexity. Simulation results demonstrate that our proposed scheme outperforms the conventional schemes.