We present a set of experimental results concerning the current noise produced during the resistive transition in a MgB2 polycrystalline thin film. Measurements of the power spectrum of the current noise, observed when the temperature is slowly changed across its critical value, are given and discussed. During the transition a large electrical noise component is generated, having a power spectrum of the 1/fn type (n ≈ 3) over a quite wide range of frequencies. This noise may be considered as generated by the abrupt creation of resistive strips across the specimen constituted by grains which have undergone the resistive transition. A computer model, based on this assumption, has been developed to simulate the resistive transition and to evaluate the noise power spectrum. The specimen has been represented as a two dimensional film characterized by randomly oriented grains having slightly different critical currents characterized by a gaussian distribution. When the temperature is incresed and reaches its critical value, resistive strips are formed according to a percolative process, giving rise to resistance steps which are at the origin of the noise. The theoretical results obtained by this model, concerning both the shape and intensity of the noise power spectrum, are compared with the experimental ones directly measured on the specimen.