The crystal structure, phase transformations and magnetic properties for Ni50-xCoxMn39Sn11 (x=0, 2, 4, 6) Heusler alloys have been systematically studied by means of structure and magnetism measurements. The results show that with increase of Co concentration, the martensitic transformation temperatures are obviously decreased, while the Curie temperatures of austenite are gradually increased, and they present different structures at room temperature. At the same time, with increasing Co content, the austenitic magnetism rapidly enhances, while the martensitic magnetism almost keeps unchanged. This leads to a significant improvement of difference magnetization (AM) between two phases. For Co content added to x=4, the value of AM between two phases achieves about 40 Am-2/kg and exhibits magnetic field- induced martensitic transformation. Using strain measurement, the strain behavior related to martensitic transition in Ni50-xCoxMn39Sn11 (x=0, 2, 4) samples was studied. It is found that the phase transition strain reaches 0.17% in Ni46Co4Mn39Sn11, sample. Within the magnetic cycles of 3 T, this sample displays a reproducible magnetostrain in temperature range of 215 similar to 235 K. Such a reproducible strain could be ascribed to the fact that a partial martensitic transformation of this sample can be driven by isothermal magnetic field.