Though the preferred welding process to weld aluminium alloy is frequently constant current gas tungsten arc welding (CCGTAW), it resulted in grain coarsening at the fusion zone and heat affected zone(HAZ). Hence, pulsed current gas tungsten arc welding(PCGTAW) was performed, to yield finer fusion zone grains, which leads to higher strength of AA6061 (Al-Mg-Si) aluminium alloy joints. In order to determine the most influential control factors which will yield minimum fusion zone grain size and maximum tensile strength of the joints, the traditional Hooke and Jeeves pattern search method was used. The experiments were carried out based on central composite design with 31 runs and an algorithm was developed to optimize the fusion zone grain size and the tensile strength of pulsed current gas tungsten arc welded AA6061 aluminium aUoy joints. The results indicate that the peak current (Ip) and base current (IB) are the most significant parameters, to decide the fusion zone grain size and the tensile strength of the AA6061 aluminum alloy joints.