Studies on propagation of electron beams in plasma have shown that in the blowout regime of the plasma wakefield accelerator (PWFA), the emittance of the incoming beam is preserved because of the linear focusing force exerted by a uniform ion column [1]. However, for positron beams the focusing force is nonlinear and they suffer emittance growth. We simulated the propagation of a positron beam in the uniform plasmas with different densities. We calculated the beam emittance from the simulation results and observed the beam size and emittance grow with increasing plasma density. Simulation results agree well with that of previous work.