The inversion of scattered waves in seismic exploration is a hot and difficult problem in related fields. We propose a hypothesis: the local wave field near each point on the wave field profile has a relationship with the minimum distance between that point and each scatterer, and this relationship can be recognized by a convolutional neural network (CNN). Based on this, the designed CNN can steadily classify and identify the scattered wavefield point by point, and realize the inversion imaging of the scatterer. We propose a new method of inversion imaging of scattered wavefield based on CNN and equivalent training model. The new method transforms the optimal inversion problem of the scatterer into the optimal design problem of the equivalent training model. Through the equivalent training model constructed by a parameterized method, the wavefield inversion and scatterer imaging of two different layered random cave media models are well realized, and the scattered wave imaging of the wavefield of the Marmousi2 model synthesis data is also realized robustly. The use of Bayesian discriminant imaging improves the resolution of the inversion results and helps interpreters quickly and accurately locate the scatterers.