The motion of a self propelling micro-organism symmetrically located in a rectangular channel containing viscous fluid has been studied by considering the peristaltic and longitudinal waves travelling along the walls of the channel. Theexpressions for the velocity of the micro-organism and time average flux have been obtained under long wavelength approximation by taking into account the viscosity variation of the fluid across the channel. Particular cases for constant viscosity and when it is represented by a step function have been discussed. It has been observed that the velocity of the micro-organism decreases as the viscosity of the peripheral layer increases and its thickness decreases.