In this paper we have developed and tested a novel method for measuring precisely the shape of pulses shorter than the acquisition step, which is effective for random delays of the input pulses with respect to the start pulse of the analogue-to-digital converter (ADC). The method is based on conversion of the short pulses to be measured into longer damped oscillations and their correct acquisition (sampling) with saving the pulse information, rearranging of the sampled oscillations with respect to some reference time instant to form a finer-discretization high-precision oscillation, and retrieving the pulse shape by inverse algorithms. We demonstrated experimentally the good performance (5–7% rms error) of this method (by using 20 MHz/8 bits ADC) when measuring the shape of randomly arriving pulses, shorter than the ADC sampling step (50 ns), with an equivalent sampling frequency up to 2 GHz (0.5 ns equivalent sampling step). The resolving of shapes in a pulse pair with an inter-pulse delay shorter than the ADC sampling interval has also been demonstrated. The limiting equivalent sampling frequency is estimated to be up to 500 GHz. This method can be effectively applied for creation of some novel short-pulse measuring techniques, avoiding the problem of time synchronization to the start pulses in lidar and radar, nuclear experiments, tomography, communications, etc.