We propose a fault detection and diagnosis (FDD) method for liquid-propellant rocket engine tests during startup transient based on deep learning. A numerical model describing the startup transient for the hot-firing test of the rocket engine allows to simulate normal and abnormal situations caused by various types of faults. Datasets containing potential fault types during the engine startup have been constructed using the numerical model to train deep neural networks targeting. Actual hot-firing ground test data of a liquid rocket have been used to determine the input parameters of the model and validate the simulation results. A numerical case study on FDD for the ground operation of an open-cycle liquid-propellant rocket engine demonstrates the effectiveness of the proposed method compared to the traditional red-line cutoff.