A three-dimensional (3D) transient inverse forced convection problem is solved in the present study using the Conjugate Gradient Method (CGM) and the general purpose commercial code CFX4.2-based inverse algorithm to estimate the unknown boundary heat flux in a three-dimensional irregular duct flow problem. The advantage of calling CFX4.2 as a subroutine in the present inverse calculation lies in that many difficult but practical 3D inverse convection problem can be solved under this construction. Results obtained by using the conjugate gradient method to solve this 3D inverse forced convection problems are justified based on the numerical. experiments. It is concluded that accurate boundary fluxes can be estimated by the conjugate gradient method except for the inlet surface and final time. The reason and improvement of this singularity are addressed. Finally, the effects of the height of duct, velocity of the inlet fluid and measurement errors on the inverse solutions are discussed.