The current-mode-counting method is a new approach to observing transient processes, especially in transient nuclear fusion, based on the non-homogeneous Poisson process (NHPP) model. In this paper, a new measurement process model of the pulsed radiation field produced by transient nuclear fusion is built based on the NHPP. A simulated measurement is performed using the model, and the current signal from the detector is obtained by simulation based on Poisson process thinning. The neutron time spectrum is reconstructed and is in good agreement with the theoretical value, with its maximum error of a characteristic parameter less than 2.3%. Verification experiments were carried out on a CPNG-6 device at the China Institute of Atomic Energy, with a detection system with a nanosecond response time. The experimental charge amplitude spectra are in good agreement with those obtained by the traditional counting mode, and the characteristic parameters of the time spectrum are in good agreement with the theoretical values. This shows that the current-mode-counting method is effective for the observation of transient nuclear fusion processes.