Turbulent plasmas are found in nature and the laboratory: examples include solar wind and fusion confinement. For fusion devices, the transport of particles and heat in a turbulent plasma state is relevant for creating an efficient fusion plasma. To achieve fusion ignition, it is necessary to minimize outward flux and keep energy at the center of a hot plasma. ITER, the next big step for the international magnetic confinement fusion program, has been designed based on estimates of transport that assume standarddiffusion by Brownian motion. By contrast, we are interested in examples of transport where the motion is non-diffusive, defined such that the variance of particle displacements does not scale linearly with time. In our simplified model of a quasi-two dimensional plasma, results from simulations of passive particles representing fast ions in a stochastic velocity field reveal non-diffusive transport dependent on temperature. These results suggest that a fractional diffusion equation gives a better description of certain types of plasma transport compared to the standard diffusion equation.