Based on the mass-energy relation in Einstein's relativity theory, thermal energy has equivalent mass, which is referred to as thermal mass. The concepts of phonon gas mass in solids and thermon gas mass in gases are then introduced. Based on these concepts, the momentum conservation equation, including driving force, resistance and inertial force, for the thermal mass motion is established using Newtonian mechanics. Since the heat conduction is just the motion of the thermal mass (phonon gas or thermon gas) in a medium, the momentum conservation equation for thermal mass is a general heat conduction law which can unify the description of heat conduction under various conditions. The momentum conservation equation reduces to Fourier's heat conduction law when the heat flux is not very high so that the inertial force of the thermal mass can be ignored. For micro-/nano_scale heat conduction, the heat flux may be very high and the inertial force due to the spatial velocity variation can not be ignored. Therefore, the heat conduction deviates from Fourier's law, i.e. non-Fourier phenomenon takes place even under steady state conditions. In such cases, the thermal conductivity can not be calculated by the ratio of the heat flux to the temperature gradient. Under ultra fast heat conduction conditions, the inertial force of the thermal mass must be taken into consideration and the momentum conservation equation for the thermal mass motion leads to a damped wave equation. Compared with the CV model, the general heat conduction law includes the inertial force due to the spatial velocity variation. Thus the physically impossible phenomenon of negative temperatures induced by the thermal wave superposition described by CV model, is elliminated, which demonstrates that the present general law of heat conduction based on thermal mass motion is more reasonable.