The main parameters that characterize the morphology quality of multi-layer and multi-pass laser metal printed parts are the surface roughness and the error between the actual printing height and the theoretical model height. This study employed the Taguchi method to establish the correlation between process parameter combinations and multi-objective characterization of metal print morphology quality (height error and roughness). The signal-to-noise ratio (SNR) and grey correlation analysis method were used to predict the optimal parameter combination for multi-layer and multi-pass printing: laser power 800 W, powder feeding rate 0.3 r/min, step distance 1.6 mm, scanning speed 20 mm/s. Subsequently, we constructed the Genetic Bayesian-back propagation network (GB-BP) to predict multi-objective responses. Compared with the traditional BP network, the GB-BP network improved the accuracy of predicting height error and surface roughness by 43.14% and 71.43%, respectively. The network can accurately predict the multi-objective characterization of the morphology and quality of multi-layer and multi-pass LDED metal printed parts.