Differential equations for Yakubovsky components are employed to calculate the parameters for low-energy nucleon-trinucleon scattering. The method of cluster reduction is used to solve numerically these equations for energies below the three-body threshold for the system in question. The scattering lengths and phase shifts in the S - 1, T = 0 and S = 0, T = 0 channels are obtained for the local nucleon-nucleon potential MTI-III. The results of the calculations agree with data obtained by other authors.