The topological nature of the quantum anomalous Hall effect (QAHE) causes a dissipationless chiral edge current at the sample boundary1,2. Of fundamental interest is whether the chirality of the band structure manifests itself in charge transport properties. Here we report the observation of large non-reciprocal charge transport3 in a magnetic topological insulator, Cr-doped (Bi,Sb)2Te3. When the surface massive Dirac band is slightly carrier doped by a gate voltage, the edge state starts to dissipate and exhibits a current-direction-dependent resistance with a directional difference as large as 26%. The polarity of this diode effect depends on the magnetization direction as well as on the carrier type, electrons or holes. The correlation between the non-reciprocal resistance and the Hall resistance indicates that the non-reciprocity originates from the interplay between the chiral edge state and the Dirac surface state.