The creep behaviour of Sn-3.0Ag-0.5Cu lead-free solder specimens with a diameter of 1.0 mm is investigated subjected to tensile forces from 10 to 25 N under electric currents ranging from 0 to 20 A. Due to the Joule heating effect, the solder temperature induced by electric current is measured to quantify the deterioration of tensile behaviour. Based on the observed steady-state creep deformation, the creep strain rate varies linearly with the tensile stress in the natural logarithmic coordinate with a stress threshold for the electric current between 0 and 10 A, and the natural logarithm of creep rate has a linear relationship with the square of current density. By revealing the dislocation climbing as the dominate creep mechanism under the coupled mechanical-electric-thermal loading, a modified Norton's model is proposed which shows exponential dependence on the square of current density and the natural logarithm of tensile stress with the stress exponent enriched as a quadratic function of current density.