The motion of a particle sliding under the action of an external field on a stochastically fluctuating one-dimensional Edwards-Wilkinson surface was studied. The results show that the motion of a passive sliding particle on a fluctuating surface may show nontrivial behavior even when the surface is Gaussian. The results also show that the the characteristic length scale shows anomalous diffusion when the surface fluctuations occur on a time scale smaller than the particle motion. The possibility of a slow crossover toward asymptotic diffusive behavior was also discussed.