The compact plate heat exchanger is a key component in the solid oxide fuel cell combined heat and power system for waste heat recovery. To address issues such as high residual stress and poor weld quality after brazing, the high-temperature brazing process of a channel unit structure in the plate heat exchanger, designed for waste heat recovery, was simulated using the finite element software ABAQUS based on thermo-elasto-plastic theory. The residual stress distribution after brazing was obtained, and process parameters on residual stress were analyzed. The results show that the residual stress distribution of the channel structure is highly complex. The axial residual stress at the brazed joint between the plate and the spacer element at the channel inlet reaches a maximum of 313.3 MPa. The most severe plate deformation occurs at the brazed joint between the cold-side flow channel plate and the rectangular spacer element, reaching 0.107 mm, which is 286.6% of that at the same position on the hot side. With a decrease in brazing cooling rate, the residual stress gradually decreases. When the cooling rate is below 30 K/min, the internal residual stress of the channel structure can be effectively reduced. When BNi-2 nickel-based filler is used, the residual stress and flowability of the filler achieve an optimal balance.