We examine the mechanical matrix model that can be derived from the SU(2) Yang-Mills light-cone field theory by restricting the gauge fields to depend on the light-cone time alone. We use Diracs generalized Hamiltonian approach. In contrast to its well-known instant-time counterpart the light-cone version of SU(2) Yang-Mills mechanics has in addition to the constraints, generating the SU(2) gauge transformations, the new first and second class constraints also. On account of all of these constraints a complete reduction in number of the degrees of freedom is performed. It is argued that the classical evolution of the unconstrained degrees of freedom is equivalent to a free one-dimensional particle dynamics. Considering the complex solutions to the second class constraints we show at this time that the unconstrained Hamiltonian system represents the well-known model of conformal mechanics with a ``strength of the inverse square interaction determined by the value of the gauge field spin.
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