An inverse design problem is solved to determine the shape of complex coolant flow passages in internal cooled turbine blades by using the conjugate gradient method (CGM). One of the advantages of using CGM lies in that it can easily handle problems having a huge number of unknown parameters and it converges very fast. The boundary element method (BEM) is used to calculate the direct, sensitivity and adjoint problems due to its characteristics of easily-handling the problem considered here. Results obtained by using the CGM to solve the inverse problems are verified based on the numerical experiments in the analysis model. One concludes that the CGM is applied successfully in estimating the arbitrary shape of cavities and the rate of convergence is also very fast even when the number of unknown parameters is large. Moreover, the design model of the inverse problem is also performed to estimate the optimal shape of cooling passages in accordance with the desired blade surface temperature distributions.