Use of laser beam in high precision joining of two dissimilar materials has become a very useful technique. It has potential application in biomedical implants and their encapsulation process. In this research, a numerical method is developed using finite element technique to determine the optimum condition of jointing two dissimilar materials namely titanium and polyimide. Non-uniform discretization with large number of elements in the areas of high temperature gradients were used. The accuracy of the current numerical model was verified by comparing sample results with experimental data and good match was found. This gave us the confidence that the current method can be used for other combination of materials. It was observed that for a particular value of the laser power, good bonding between the dissimilar materials is a function of laser scanning speed. Too high speed will not produce any significant increase in temperature at the bimaterial interface to have a good chemical bonding. On the other hand, too slow speed will cause excessive increase in temperature resulting in burnout condition for polyimide. For the ranges of parameters investigated in the current study, it was observed that for a leaser heat flux of 4.0 W, good bonding occurs for a laser scanning speed between 600 and 2000 mm/min. It was also observed that increased scanning speed causes the temperature contour to stretch in the horizontal direction.