The shape optimal design of the plate-fin type heat sink with vortex generator is performed to minimize the pressure loss subjected to the desired maximum temperature numerically. Evaluation of the performance function, in general, is required much computational cost in fluid/thermal systems. Thus, global approximate optimization techniques have been introduced into the optimization of fluid/thermal systems. In this study, Kriging method Is used to obtain the optimal solutions associated with the computational fluid dynamics (CFD). The results show that when the temperature .rise is less than 40 K, the optimal design variables are $B_1=2.44;mm,;B_2=2.09;mm$, and t=7.58 mm. Kriging method can dramatically reduce computational time by 1/6 times compared to SQP method so that the efficiency of Kriging method can be validated.