The ultrasonic Pulse-Echo method plays a significant role in ultrasonic thickness measurement. However, when the measured thickness is relatively thin, it is universal for the reflected ultrasonic echoes to overlap in the time domain which constrains the achievable resolution using the conventional Pulse-Echo method. A deep learning network for multi-echo overlapping ultrasonic signals separation under the constraint of an ultrasonic transducer with specific center frequency and bandwidth was proposed to enhance the axial resolution. With this model, the adaptive separation of overlapping signals with an unknown number of echoes is achieved by extracting detailed features of the overlapping signals. An overlapping signal training dataset based on truncated Nakagami functions is constructed to train the network. Simulation experiments under different degrees of overlap and noise levels were conducted for the performance analysis. Simulation results manifested the performance advantage of proposed separation method over some traditional separation methods. Further, ultrasonic thickness measurement experiments were performed on thin-walled aluminum alloy plates with various thicknesses, demonstrating feasibility and practicability of the network over traditional separation methods.