We experimentally and numerically investigated the chaos synchronization characteristics of mutually coupled semiconductor lasers (MCSLs) with asymmetrical bias currents. Experimental results show that, asymmetrical bias current level of two MCSLs has obvious influence on chaos synchronization between them, and stable leader-laggard chaos synchronization can be realized under relatively large asymmetrical bias current levels. Moreover, the influences of frequency detuning and mutually coupling strength between the two lasers on chaos synchronization performance have also been discussed. Theoretical simulations basically conform to our experimental observations.