We studied the magnetostriction of Nd6Fe13−xCoxSi (x = 0, 1) intermetallic compounds with tetragonal Nd6Fe13Si-type structure, using the strain gauge method in the temperature range of 77–600 K under applied magnetic fields up to 1.5 T. The anisotropic magnetostriction (Δλ) versus temperature of the studied samples has shown almost similar field-dependence behavior. Below the spin reorientation temperature (TSR), Δλ changes its sign from positive to negative value at an applied threshold field which increases with decreasing temperature. This behavior may originate from the reduction of the magnetocrystalline anisotropy with temperature. It is also observed that absolute value of Δλ increases by Co substitution. On the other hand, the volume magnetostriction (ΔV/V) versus field shows different behavior. The ΔV/V curves of Nd6Fe12CoSi tend to have a nearly quadratic dependence on applied field near magnetic ordering temperature as expected for the parastrictive behavior. The temperature dependence of magnetostriction values is discussed based on the magnetostriction relation of the tetragonal structure to determine the signs of some of magnetostriction constants for these polycrystalline compounds.