The aim of this paper is to present a boundary-layer analysis of two-phase dusty non-Newtonian fluid flow along a vertical surface by using a modified power-law viscosity model. This investigation particularly reports the flow behavior of spherical particles suspended in the non-Newtonian fluid. The governing equations are transformed into non-conserved form and then solved straightforwardly by implicit finite difference method. The numerical results of rate of heat transfer, rate of shear stress, velocity and temperature profiles and streamlines and isotherms are presented for wide range of Prandtl number, i.e., 0.7 <= Pr <= 1000.0, with the representative values of the power-law index n. A good agreement is found between the present and the previous results when compared for some special cases. The key observation from the present study is that the power-law fluids with (n > 1) are more likely to promote the rate of heat transfer near the leading edge. (C) 2017 Elsevier Ltd. All rights reserved.