In this study, the generalised velocity slip and the generalised temperature jump of nanofluid in the flow over a stretching sheet with variable thickness are investigated. Because of the non-adherence of the fluid to a solid boundary, the velocity slip and the temperature jump between fluid and moving sheet may happen in industrial process, so taking velocity slip and temperature jump into account is indispensable. It is worth mentioning that the analysis of the velocity v , which has not been seen in the previous references related to the variable thickness sheet, is presented. The thermophoresis and the Brownian motion, which are the two very important physical parameters, are fully studied. The governing equations are simplified into ordinary differential equations by the proper transformations. The homotopy analysis method (HAM) is applied to solve the reduced equations for general conditions. In addition, the effects of involved parameters such as velocity slip parameter, temperature jump parameter, Prandtl number, magnetic field parameter, permeable parameter, Lewis number, thermophoresis parameter, and Brownian motion parameter are investigated and analysed graphically.