This paper provides a cognitive space-time (angle-Doppler) transmit pattern design method for mitigating clutter effect. This pattern takes full advantage of degrees-of-freedom (DOF) on transmit, which can preserve the maximum response for the target of interest while prenulling the mainlobe clutter on transmit, potentially simplifying processing on receiver and reducing the requirement for receiver dynamic range. The output signal-to-clutter-and-noise ratio (SCNR) can be improved significantly after applying the cognitive space-time transmit pattern to airborne-phased array radar. In addition, the traditional transmit antenna pattern and the proposed cognitive scheme are compared in terms of the probability of target detection. Simulations are conducted to demonstrate proof-of-concept.