Summary: Image reconstruction of EIT mathematically is a typical nonlinear and severely ill-posed inverse problem. Appropriate priors or penalties are required to enable the reconstruction. The commonly used \(l_2\)-norm can enforce the stability to preserve local smoothness, and the current \(l_1\)-norm can enforce the sparsity to preserve sharp edges. Considering the fact that \(l_2\)-norm penalty always makes the solution overly smooth and \(l_1\)-norm penalty always makes the solution too sparse, elastic-net regularization approach with a convex combination term of \(l_1\)-norm and \(l_2\)-norm emerges for fully nonlinear EIT inverse problems. Our aim is to combine the strength of both terms: sparsity in the transform domain and smoothness in the physical domain, in an attempt to improve the reconstruction resolution and robustness to noise. Nonlinearity and non-smoothness of the generated composite minimization problem make it challenging to find an efficient numerical solution. Then we develop one simple and fast numerical optimization scheme based on the split Bregman technique for the joint penalties regularization. The method is validated using simulated data for some typical conductivity distributions. Results indicate that the proposed inversion model with an appropriate parameter choice achieves an efficient regularization solution and enhances the quality of the reconstructed image.