Low-resolution analog-to-digital converter (ADC), especially one-bit ADCs, is of great importance for large-scale systems due to its significant advantages, e.g., low hardware cost and low power consumption. In this paper, the problem of receive filter design for multiple-input multiple-output (MIMO) radar with one-bit ADCs is investigated. With deterministic noise distribution parameters and target scattering coefficient, the probabilities of detection and false-alarm for MIMO radar with one-bit ADCs are derived, and then the receive filter is obtained by maximizing the probability of detection subject to a fixed false-alarm. In addition, we define a quantized signal-to-noise ratio (QSNR) for MIMO radar with one-bit ADCs, and evaluate the performance difference between one-bit and infinite-bit quantizations from the SNR point of view. For imperfect scenario where the noise distribution parameters are unknown, a one-bit observation based method is devised to estimate the mean and variance of the noise. Moreover, we study the effect of unknown target scattering coefficient on the performance of the designed receive filter in terms of the QSNR, and propose robust methods to overcome this uncertainty. Finally, several representative simulations are presented to demonstrate the effectiveness of the proposed methods.