1DT is a typical post Doppler space-time adaptive processing method, and the method can significantly reduce the demand for independent identically distributing to the samples and the amount of calculations for spacetime adaptive processing. However, being poor in the process of the mainlobe clutter suppression in the temporary domain, a filter design algorithm with weighted sparse constraints by using the sparse characteristics of the filter frequency response is proposed. A sparse constraint on the sidelobe is added to the model of the time domain filter, and a weighting matrix is constructed to shape the frequency response of the mainlobe clutter. The simulation experiments show that this method can reduce the sidelobe response under condition of effectively suppressing the mainlobe clutter presupposition, and is robust with the presence of array amplitudephase error.