Friction stir welding is a new and effective solid-state welding process for joining dissimilar materials such as aluminum (Al) and copper (Cu). Joint quality of the friction stir welded materials gets influenced by the welding strategy and different friction stir welding process parameters, i.e. rotational speed, welding speed, tool design, tool pin offset, and tilt angle. In this paper, the effect of combination of different friction stir welding process parameters during joining of Al-6101 and pure copper is studied using Taguchi L18 orthogonal array. Four friction stir welding process parameters, i.e. shoulder diameter (A), pin offset (B), welding speed (C), and rotational speed (D) each at three levels except shoulder diameter, which is at two levels are selected. The effect of different combinations of these parameters on ultimate tensile strength and micro-hardness of the joints is investigated. Subsequently, single response optimization for ultimate tensile strength and micro-hardness and multi-response optimization of ultimate tensile strength and micro-hardness taken together is carried out to obtain the optimal combination of the friction stir welding process parameters. Taguchi method is used for single response optimization, whereas Taguchi-based TOPSIS method is employed for multi-response optimization. For single optimization, the optimum combination of the friction stir welding parameters yielding maximum strength and micro-hardness are A1B1C2D2 and A2B1C2D3, respectively. The optimum combination of the process parameters for multi-response optimization is A2B1C2D2. From the results of the study for single- and multi-response optimization, it is revealed that the rotational speed is the most significant process parameter affecting the tensile strength and micro-hardness of the joints followed by the welding speed. Further, the macro/microstructure and micro-hardness profile of the joint obtained at the optimal combination of the multi-response optimization are given and discussed for better understanding of material mixing and joining.