General Purpose Graphics Processing Unite (GPGPU) allows the user to utilize GPU for general computing purposes. Using these processors can cause a great speedup in numerical calculations. Several studies have been performed to investigate the advantages of using the GPGPU in numerical calculations including solving tridiagonal set of equations. The main focus of the mentioned studies was on improving parallel methods for example CR and PCR algorithms. Although these algorithms are consistent with GPU architecture, they have higher arithmetic complexity compared with serial Thomas algorithm and also they have limitations in dimensions of the equations’ set. Therefore, in the present study, according to the advantages of Thomas algorithm compared with the parallel algorithms, a novel method entitled checkerboard Thomas has been developed to accommodate Thomas algorithm for running on GPU. This method has been used for solving 2D steady heat conduction problem and the results show an increase in the solution precision compared to Thomas and PCR algorithms. Also the results indicate that the new algorithm can cause to computing speedup between 5.7 to 22.2x, compared with Thomas algorithm. Furthermore, results show that the new method is about 2x faster than PCR algorithm. Also it has been seen that speed decrement for uncoalesced access to global memory is 42.7% in minimum and 81.9% in maximum for 128×128 and 1024×1024 grid size, respectively.