The structural, electronic and magnetic properties in bulk and various (0 0 1) surfaces of X2CoIn (X = Ti, Zr) Heusler alloy have been investigated by spin-polarized first-principles calculations. The InIn termination is the most stable one and the XIn termination is the second only to InIn termination as the most stable surface, with high spin polarizations 65.2% and 62.3% for X = Ti (80.8% and 69.6% for X = Zr), respectively. The atomic partial density of states (APDOS) and atomic magnetic moments (AMMs) of atoms in the central layer of X2CoIn (0 0 1) surface accord well with those of the corresponding atoms in bulk X2CoIn structure. The half-metallic (HM) feature is destroyed by the surface states for all the five CoCo, XCo, XX, XIn and InIn terminations. The total magnetic moment is contributed by atoms in all layers for Ti2CoIn (0 0 1) surface while is mainly contributed by the atoms in the fourth to central layers (L-4 to L-9) for the ZrIn termination but is mainly contributed by the atoms in the sixth to central layers (L-6 to L-9) for the InIn termination for Zr2CoIn (0 0 1) surface. Further experimental efforts are expected to fabricate the X2CoIn thin films and investigate the structural, electronic and magnetic properties of them.