A modified micromorphic continuum model is proposed for granular materials based on a micromechanics approach. In this model, a continuum material point is considered as a granular volume element whose deformation behavior is influenced by the translation and the rotation of particles. And a hypothesis is proposed that the microscopic actual motion is decomposed into a microscopic average motion and a fluctuation related to the average motion. By symmetric correction of micro curvature, a symmetric Cauchy stress and a symmetric couple stress conjugated with a symmetric strain and a symmetric curvature respectively, and asymmetric relative stress measures conjugated with asymmetric relative strain measures are obtained. Based on this decomposition and the symmetry correction, first-order micromorphic constitutive relationships are derived for granular materials with inclusion of stress-strain relation, even stress-micro curvature relation and relative stress-strain relation. Furthermore, the macroscopic constitutive moduli in the micromorphic model are obtained in the expressions of the microstructural information such as the contact stiffness and the internal length.