Multiple-input multiple-output (MIMO) systems which deploy one-bit DACs are at-tractive in many fields, such as wireless communications and radar. In this paper, the problem of transmit waveform design in MIMO radar system with one-bit DACs is investigated. By appropri-ately designing the transmitted QPSK signal waveforms, the majority of radiated energy can be fo-cused into the mainlobe region(s) by minimizing the integrated sidelobe to mainlobe ratio (ISMR) of beampattern, such that the intensity of backscattered signals from targets can be enhanced. However, the resulting optimization problem which consists of constrained fractional quadratic problem (CFQP) is noconvex. To tackle this problem, a block-sparse semidefinite relaxation meth-od is first utilized to reformulate the CFQP into a reduced convex semidefinite programming (SDP). Further, a customized interior point algorithm (IPA) is developed to solve the small-scale SDP. Finally, the desirable one-bit transmit waveform sequence can be properly synthesized by us-ing Gaussian randomization method. Numerical simulation results demonstrate that the proposed method offer better performance than the state-of-the-art algorithms.