A theoretical model which can reflect the weakening constraint power of the ductile matrix in the course of creep deformation is established to estimate the development of transient and steady-state creep strain of a fiber-reinforced metal-matrix composite. This method makes use of the secant moduli of the elastic-creeping matrix in the construction of a linear comparison composite, and, when coupled with an energy approach recently proposed by Qiu and Weng (1992, J. appl. Mech., 59, 261–268), it can also account for the effect of non-uniform stress fields on the overall creep to a certain extent. The theory is applied to a Borsic/aluminium system to examine the anisotropic creep behavior along the axial and transverse directions. As compared to the predictions of Zhu and Weng's (1990, Mech. Mater. 9, 93–105) mean-field theory and Wang and Weng's (1992, ASME J. Engng Mater. Tech. 114, 237–244) local theory (both were based on the elastic constraint and were intended for the small creep range), the results are close to both along the axial directions, but along the transverse direction the secant-moduli method is found to provide a softer response for the composite. A direct comparison to the experimental data under transverse tension shows that the theory is quite accurate even at 35% of fiber volume fraction. The theoretical model is finally employed to estimate the growth of the maximum interfacial tensile stress under a transverse loading with and without a superimposed lateral compression, and it is found that, such a local tension, which is responsible for the onset of interfacial cracking, can grow quite significantly during the creep process, especially with the assistance of the lateral compression.