A level-set method for the numerical simulation of incompressible two-phase flow is developed for flows with moving contact lines. The method is used to study shear flow past a two-dimensional droplet that adheres to a solid substrate. Cases with pinned and moving contact lines can be simulated. Previous work on this problem assumed Stokes flow, whereas the present method is suitable for flow with significant Reynolds number. Results were found to agree well with those published previously for creeping flow. The wake formed at intermediate Reynolds numbers is located at some distance behind the droplet, because the fluid rotates in the same direction inside the wake as inside the droplet. If the contact lines are allowed to move, the wake moves with the droplet. Results will be presented for critical dimensionless parameters, beyond which part of the droplet is sheared off.