In this work, the study of fluid flow and heat transfer characteristics of a magnetohydrodynamic (MHD) fluid over a stretching plate in steady state in the presence of magnetic field is conducted. The viscosity of the fluid is assumed to vary as a linear function of temperature given by the following relation: mu = mu* [a + b(T-w - T)]. For the research of fluid flow and heat transfer in boundary layers, one usual way to treat the governing partial differential equations (PDEs) is to transform the PDEs into ordinary differential equations (ODEs). While, in the present work, the governing PDEs are kept their originals and only transformed into dimensionless forms. After that, the equations are solved directly by Chebyshev collocation spectral method (CSM) and the effects of more factors on heat transfer and fluid flow can be investigated. Effects of the variable viscosity parameter b, the Hartmann number Ha, and the Prandtl number Pr on the fluid flow and heat transfer characteristics are investigated. (C) 2015 Elsevier Ltd. All rights reserved.