Turbulence spreading in reversed shear plasmas is investigated using a simple, multi-fluid model of ITG turbulence in toroidal geometry. The temperature profile modification is accompanied by avalanche processes. In addition, it is found that the turbulence spreads inwards and outwards, owing to the nonlinear interactions of turbulence. Analysis of the simulation results indicates that the spatio-temporal propagation of the turbulence front is quantitatively consistent with the scaling of speed predicted by the Fisher front theory.