An analysis is made for a deforming gas bubble impulsively started to rise with a constant velocity in a quiescent liquid of infinite extent. The disturbed layer is sufficiently large and thus makes possible an important simplification of the governing equations of motion. Simultaneous solution of the unsteady boundary-layer equations for the both outside and inside flows of the bubble are obtained by considering that tangential velocity components and shear stresses on both sides of the interface are equal, while the normal velocity components are given by the velocity of growing of the bubble. Satisfactory results are obtained for spherical deforming air bubbles in water. The theoretical results are applicable to any uniformly deforming fluid sphere started impulsively in a substantially immiscible, viscous liquid provided that the internal circulation is complete, the flow separation is negligible and the Reynolds number is sufficiently large.