A new approach to deduce the effective viscosity of bubbly liquid with considering non-equilibrium bubble deformations in transient shear flows was proposed. Simultaneous measurement of the bubble shape and the spatio-temporal velocity distribution clarified that bubble deformation has delay from a variation of the local Capillary number under a transient process of flows from a stationary state to a rigid body rotation (spin-up) in a rotating cylinder. Relative viscosity of the bubbly liquid against the single phase condition estimated by the proposed method shows 60 % increase as the maximum. Such large increase of the effective viscosity cannot be introduced by mixture of spherical bubbles and bubbles with equilibrium deformations, and thus the non-equilibrium bubble deformations take a primary role on the modification of the effective viscosity in unsteady shear flows.