To achieve multi-objective aerodynamics design optimization for a 1.5-stage transonic compressor, a design platform incorporating blade parameterization methods, a BPNN surrogate model, and the NSGA-II optimization method was developed. The stagger angle distribution of three blade rows was selected as the optimization variable, with isentropic efficiency at the new design condition and stall margin set as the goal functions. Results demonstrated that, without altering the blade profile shape and endwall contour, the flow rate at design condition increased by 7.1%, stall margin increased by 1.8%, isentropic efficiency decreased by 0.0087, and total pressure ratio experienced a slight increase. The flow field at different conditions before and after optimization was compared and analyzed. The analysis indicated that the tangential velocity of rotor outlet becomes the determining factor for the compressor’s work capacity. The relative Mach number at the rotor inlet emerged as the key parameter affecting shock wave intensity and shock wave/boundary layer interaction, which directly influenced the efficiency of the rotor passage. At near stall condition, the stator vane root’s stagger angle is crucial for the compressor’s performance.