We report the observation of large exchange bias (EB) in Ni50-xCoxMn38Sb12 Heusler alloys with x = 0, 2, 3, 4, 5, which is attributed to the coexistence of ferromagnetic (FM) and antiferromagnetic (AFM) phases in the martensitic phase. The phase coexistence is possibly due to the supercooling of the high temperature FM phase and the predominant AFM component in the martensitic phase. The presence of EB is well supported by the observation of the training effect. The EB field increases with Co concentration. The maximum value of 480 Oe at T = 3 K is observed in x = 5 after field cooling in 50 kOe, which is almost double the highest value reported so far in any Heusler alloy system. Increase in the AFM coupling after Co substitution is found to be responsible for the increase in the EB.