A sequential functional specification method was adopted to identify the surface heat flux in a two-dimensional inverse heat conduction problem for an orthotropic solid. The inverse problems were solved with the combination of the finite control volume method, the Newton-Raphson method, and the concept of future time step.The undetermined heat flux at each time step was denoted as one of the unknown variables in a set of nonlinear equations, which was solved by an iterative process. Results show that the estimated values agree well with the exact values in the examples, which proves that this method is an accurate, stable, and efficient one, thus it can be used to determine the surface heat flux in two-dimensional nonlinear inverse heat conduction problems.