This paper presents a comprehensive approach for modeling and classification of air gap asymmetry and inter-turn short circuit faults in ladder-secondary linear induction motors (LS-LIMs). It is based on a modified Magnetic Equivalent Circuit (MEC) model incorporated with a current signal-based fault detection method using Convolution Neural Network (CNN). The feature sets of the mentioned faults are classified separately by a CNN, and the training and test data are extracted using three-phase currents obtained from MEC. For this purpose, both healthy and faulty motors are modeled initially by the proposed MEC model to generate different labeled data for training the designed CNNs. It is also shown that fault diagnosis of this motor by Fast Fourier Transform (FFT) is not possible. Finally, the proposed networks are trained based on the obtained currents from Finite Element Method (FEM) to validate their accuracy. Since faults diagnosis in LS-LIMs based on CNN has not been introduced in the relevant literature so far, it is presented in this paper for the first time.