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This paper presents the lowest-order weak Galerkin finite element method for linear elasticity problems on the convex polygonal meshes. This method uses piecewise constant vector-valued spaces on element interiors and edges. The discrete weak gradient space introduced by this paper is the matrix version of C W 0 space. The discrete weak divergence space is piecewise constant space on each element. This method is simple, efficient, stabilizer-free and symmetric positive-definite. The optimal error estimates in discrete H 1 and L 2 norms are presented. Numerical results are given to demonstrate the efficiency of algorithm and the locking-free property. • The matrix version of C W 0 element for discrete weak gradient is introduced. • The lowest-order weak Galerkin finite element space ( P 0 2 , P 0 2 , C W 0 2 , P 0 ) is adopted. • Our method is suitable for the polygonal and hybrid meshes. [ABSTRACT FROM AUTHOR]