In this paper, we propose a null space-based precoding scheme for secondary transmission in a cognitive radio multiple-input multiple-output (CR-MIMO) network under the assumption that time-division-duplex is employed by the primary transmission. First, the secondary transmitter periodically senses the transmitted signals from the primary users and estimates the corresponding covariance matrix. Then, subspace techniques are utilized to estimate the noise subspace of this covariance matrix, and the dimension of the noise subspace is estimated using information theory criteria (AIC or MDL). Finally, the obtained null space is used as the precoding matrix for the secondary transmission, which effectively avoids the interference induced by the secondary transmission at the primary users. Moreover, the achievable capacity of the secondary MIMO channel by the proposed scheme is derived. Simulations are performed to show the efficacy of the proposed scheme.