The present paper introduces q-analogues of the Sumudu transform and derives some distinct properties, for example its convergence conditions and certain interesting connection theorems involving q-Laplace transforms. Furthermore, certain fundamental properties of q-Sumudu transforms like, linearity, shifting theorems, differentiation and integration etc. have also been investigated. An attempt has also been made to obtain the convolution theorem for the q-Sumudu transform of a function which can be expressed as a convergent infinite series.