A shell and tube heat exchanger with staggered baffles (STHX-ST) is designed by integrating the features of both segmental and helical baffles, which produces a helical flow in the shell side. This work studies the effect of different parameters on the performance of the STHX-ST through numerical analysis. Shell inner diameter, tube outer diameter, baffle cut, baffle spacing, and baffle orientation angle are the design parameters. Multi-objective optimization using genetic algorithm (GA) is carried out to maximize the heat transfer rate while minimizing the pressure drop. The objective functions for optimization are approximated using artificial neural networks (ANNs). The training data for ANNs are simulated from CFD analysis as per the Taguchi orthogonal test table. The optimal solution obtained from the Pareto front has a maximum heat transfer of 154555 W for a minimum pressure drop of 88083.86 Pa.