Summary: The regularity of very weak solutions \(u(x)\in W^{1, r}_{\text{loc}}(\Omega, \mathbb{R}^N)\) for a class nonlinear elliptic systems \(\text{div} A(x,u,Du)= B(x,u,Du)\) is discussed on a bounded open set \(\Omega \subset \mathbb{R}^n (n\geq 2)\), where \(A(x,u,Du)\) satisfies the coercive and growth conditions, \(B(x,u,Du)\) satisfies controllable growth conditions, \(\max\{1,p-1\} <r<p,p\) appears in the coercive and growth assumptions for the operators \(A\) and \(B\). Here Hodge decomposition is used to construct a suitable test function, the reverse Hölder inequality for very weak solutions of the elliptic systems is proved. It is also shown that \(u(x)\) is a weak solution in the usual sense.