Kirchhoff prestack time migration (PSTM), which works trace-by-trace, remains appealing to academia and industry due to its robustness and efficiency. However, like the other prestack migration methods, Kirchhoff PSTM also suffers from the angle-dependent stretching effect, which narrows the amplitude spectra of seismic data. This effect gets more severe as the incident angle increases. In this paper, we propose a novel approach, which attaches a prediction shaping filter to the Kirchhoff PSTM, to mitigate the stretching effect. Our approach takes advantage on the trace-by-trace implementation of the PSTM algorithm, without the output of the angle-domain common-imaging gather (ADCIG). Also, our method can cascade with Q-compensation in PSTM. We examine our method with numerical examples and one field data.