PTFM (Pulse Train Frequency Modulation) waveform is widely used in active sonar, which consists of the same LFM (Linear Frequency Modulation) waveform. However, the time sidelobe level of PTFM is high, which affects multi-target discrimination. Therefore, the LFM-Costas waveform is proposed by LFM frequency encoded with the Costas sequence to solve the problem of high time sidelobe level. However, the correlation Doppler sidelobe level of the LFM-Costas waveform is high, which affects the target Doppler estimation. In order to find a waveform with high time resolution and Doppler resolution, LFM-Costas-T is proposed. This waveform pulse width Costas sequence coding for LFM weakened the Doppler correlation sidelobe level, and obtains the sharp ambiguity function (AF). Thus, the LFM-Costas-T waveform not only has high time resolution and low time sidelobe level, but also has better Doppler resolution compared with PTFM and LFM. In addition, the sharp AF of LFM-Costas-T makes it easier for multi-target discrimination and low-speed target detection in the reverberation environment.