Printed Circuit Heat Exchanger (PCHE) is a widely used heat exchanger in the supercritical carbon dioxide (sCO2) Brayton cycle because it can work under high temperature and pressure, and has been a hot topic in Next Generation Nuclear Plant (NGNP) projects for use as recuperators and condensers. Most previous studies focused on channel structures or shapes. However, no clear advancement has so far been seen in the allover size of the PCHE. In this paper, we proposed an optimal size of the PCHE with a fixed volume. Two boundary conditions of PCHE were simulated, respectively. When the volume of PCHE was fixed, the heat transfer rate and pressure loss were picked as the optimization objectives. The Pareto front was obtained by the Multi-objective optimization procedure. We got the optimized number of PCHE channels under two different boundary conditions from the Pareto front. The comprehensive performance can be increased by 5.3% while holding in the same volume. The numerical results from this study can be used to improve the design of PCHE with straight channels.