The compound Fe1-x Cox Si is a good representative for a cubic magnet with Dzyaloshinskii-Moriya interaction. On the basis of the neutron diffraction and superconducting quantum interference device measurements, we built the H-T phase diagram for the compound with different x from 0.1 to 0.7. The same set of parameters governs the magnetic system for different x. These parameters are well interpreted in the framework of the recently developed theory. As a result, the spin-wave stiffness, the Dzyaloshinskii constant, the anisotropic exchange constant, and the spin-wave gap caused by the Dzyaloshinskii interaction have been obtained and plotted as a function of x. The changes of the magnetic structure with x can be well interpreted on the basis of our findings.