We study reconstruction of the chiral edge states in a magnetic Chern insulator in the Kondo lattice model on a triangular lattice at 1/4 filling. In this state, the spin scalar chirality associated with a four-sublattice noncoplanar magnetic order assures the topological nature characterized by a nonzero Chern number. Performing a Langevin-based numerical simulation for finite-size clusters with the open boundary condition in one direction, we clarify how the magnetic and electronic properties are modulated near the edges of the system. As a result, we find that the magnetic state near the edges is reconstructed to develop ferromagnetic spin correlations. At the same time, the electronic state is also modified and the chiral edge current is enhanced. We discuss this enhancement from the viewpoint of the electronic band structure for the gapless edge states.