The study describes an approach for simulating non-Fourier heat conduction with phase change using a hyperbolic lattice Boltzmann method (HLBM). Unlike the commonly used lattice Boltzmann method (LBM), the HLBM uses a hyperbolic collision operator and modifies the equilibrium distribution function for the temperature to handle the latent-heat source term. The use of HLBM in this study enables the recovery of the enthalpy conservation equation and avoids the need for iteration stages or solving groups of linear equations, making the approach more efficient and accurate. The study suggests that the approach is more efficient and accurate than previous methods and can be used to simulate complex thermal processes involving phase change. The method could be useful in various applications, such as in the design of efficient heat exchangers or in understanding the behavior of materials during phase transitions.