For the three-dimensional transient heat conduction problem, considering the internal heat source. The dual reciprocity boundary element method (DRBEM) combined with the precise integration method (PIM) is used to solve the problem. According to the governing equation of transient constant coefficient heat conduction problem in isotropic medium with internal heat source, the corresponding boundary integral equation is derived by the weighted residual method. The dual reciprocity method (DRM) is applied to deal with the obtained boundary integral equation. The domain integral caused by the heat source term and the time derivative term of temperature is transformed into the boundary integral after being approximated by radial basis function (RBF). Then, the boundary integral equation is discretized to obtain the first-order constant coefficient differential equations related to time. Finally, in the process of obtaining the analytical solution, the matrix exponential function (MEF) is processed by PIM. Three numerical examples are given to verify the accuracy and stability of the method.