We present two-dimensional numerical simulations of thermo-compositional convection to test the hypothesis that the combined buoyancy from both thermal and salinity contrasts in Europa's ice shell can produce the numerous uplifts and pits on Europa's surface. Our simulations show that uplifts and pits with amplitude of 100--500 m and diameters of 10--30 km (similar to some of the observed features) can be produced in a 10--30 km-thick ice shell with 2--10% compositional density variations if the viscosity contrast due to temperature variation does not exceed 106. The pit and uplift formation time and lifetime are approximately proportional to the surface viscosity, ranging from 104 years to 107 years for viscosity contrasts of 104--106. Convection cannot produce substantial surface topography if the viscosity contrast exceeds 107--108. These results imply that thermo-compositional convection can only produce Europa's pits and uplifts if Europa's surface is weak.