We present a deep, wide-field optical survey of the young stellar cluster Alpha Per, in which we have discovered a large population of candidate brown dwarfs. Subsequent infrared photometric follow-up shows that the majority of them are probable or possible members of the cluster, reaching to a minimum mass of 0.035 Msun. We have used this list of members to derive the luminosity and mass functions of the substellar population of the cluster (alpha =0.59+/-0.05, when expressed in the mass spectrum form phi ~ M-alpha ) and compared its slope to the value measure for the Pleiades. This comparison indicates that the two cluster mass functions are, indeed, very similar. Based on observations collected with the Kitt Peak National Observatory, USA, and the Hispano-German Observatory of Calar Alto, Spain.