Abstract: Conjugate heat transfer is widely present in the fields of science and engineering. With the development of computing power, the accurate and effective numerical simulation of conjugate heat transfer has become a major challenge in scientific research and engineering design. The method of numerical simulation of conjugate heat transfer can be divided into two main categories: partitioned method and monolithic method. Each of these methods has its pros and cons. We have developed a monolithic method for simulating the conjugate heat transfer between solid and incompressible laminar flows with the finite element method. Heat conduction in solid is solved by the standard Galerkin finite element method. The flow solution adopts the characteristic-based split finite element method (CBS). This method is an important finite element method for solving flow problems, and equal-order finite elements can be used. Compared with semi-implicit and CBS-AC schemes, the quasi-implicit scheme of this method can adopt a larger time-step. The stability of the quasi-implicit scheme is improved by distinguishing the time step in the stabilization item from the global time step. Based on the quasi-implicit scheme of the improved CBS method, a monolithic method of conjugate heat transfer numerical simulation has been developed. In this way, the fluid part and solid part of the computational domain can be divided into finite element meshes as a whole, and the equal-order interpolation functions can be used for all variables, thus facilitating the realization of the program. The accuracy of this method is validated by simulating the benchmark problems. The effect of the time step for the solid domain on the convergence of steady conjugate heat transfer simulation has also been studied.