A solution method has been discussed for solving fluid flow and heat transfer problems in complex geometries. The solution procedure is based on finite volume method in the curvilinear coordinate system. Non–staggered grid system has been adopted to store the variables. Cartesian velocity components are considered as the dependent variables in momentum equations. Convective terms have been discretized by first order upwind scheme and diffusive terms by central difference method. SIMPLE solution procedure developed for the Cartesian coordinate system has been extended to present curvilinear coordinate system. In order to demonstrate the capability of solution method, laminar flow in 3D ducts of various cross sections (circular, elliptic, triangular, trapezoidal, rhombic, sine) are considered as test problems. Results obtained from present solver are compared with results reported by Shah and London [1]. The comparison indicates that the present solution method can be successfully used to predict fluid flow problems in complex geometries.