Single-crystalline thin film of Ni46Co4Mn37In13 alloy grown on MgO(0 0 1) was prepared by Pulsed Laser Deposition (PLD) method. The epitaxial growth process was monitored by in situ Reflection High Energy Electron Diffraction (RHEED). Structure measurements reveal that the single-crystalline Ni46Co4Mn37In13 film could be stabilized on MgO(0 0 1) as a face-centered-cubic (fcc) structure. From the evolution of RHEED, it can be deduced from the patts that Volmer-Weber growth mechanism (3-D) dominates at the initial stage. Then, it becomes layer-by-layer growth mechanism (2-D) with the increase of the film thickness. Lastly, growth mechanism converts back to 3-D when the film is thick enough. Both electrical resistance and magnetoresistance (MR) were measured at various temperatures using Physical Property Measurement System (PPMS). The electrical resistance measurement indicates that the film sample does not have martensitic transformation in the measurement temperature range. However, with the temperature increasing, the film sample exhibits a transition from metallic to semiconductor-like properties. Moreover, a small negative magnetoresistance was observed at different temperature, which can be explained by the spin-dependent scattering of the conduction electrons.