The relationship between the temporal coherence (i.e. the coherence length) and the output power of a multi-longitudinal mode Ar+ laser is studied. The experimental measurements show that the coherence length behaves a hyperbola as a function of the output power. A simple model of multimode equal amplitude power spectrum is employed in the theoretical analysis. Good agreement between theory and experiment is obtained, It is shown that for a multi-longitudinal mode Ar+ laser, the product of the coherence length and the output power is almost a constant.