In the current paper, we investigate the existence and regularity of weak solutions to a class of non-uniformly elliptic equations with degenerate coercivity and non-polynomial growth. The model case is given as follows: div exp(1 + |Du|) (1 + |u|) 2 Du + M(|Du|) (1 + |u|) 2 .u = f in ω. An L ∞-estimate of solutions is also obtained for an L 1-datum f.