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The paper is concerned with numerical modelling of the homogeneous magnetohydrodynamic turbulence decay based on large eddy simulation (LES). The modelling of the turbulent process is based on the solution of a filtered unsteady three-dimensional Navier-Stokes equation and on the equation of magnetic field strength. A dynamic model has been applied to derive the main equations. The problem is solved numerically: the equation of motion is solved by a modified method of fractional steps using compact schemes; the equation for pressure is solved by the Fourier method with a combination of matrix factorization; the equation for magnetic field is solved by the method of fractional steps. The variation of the kinetic and magnetic energies of turbulence with time was obtained depending on the medium conductivity properties. Patterns are defined for micro- and macro-scale turbulence, longitudinal and transverse correlation functions as well as for the Taylor micro-scale Reynolds number for velocity and magnetic field. [ABSTRACT FROM AUTHOR]