In this paper, we first give the definition of degenerate weakly ($k_1$, $k_2$-quasiregular mappings by using the technique of exterior power and exterior differential forms, and then, by using Hodge decomposition and Reverse H$"{o}$lder inequality, we obtain the higher integrability result: for any $q_1$ satisfying 0 < $k_1({n atop l})^{3/2}n^{l/2};{ imes};2^{n+1}l;{ imes};100^{n^2};[2^l(2^{n+3l}+1)];(l-q_1)$ < 1 there exists an integrable exponent $p_1$ = $p_1$(n, l, $k_1$, $k_2$) > l, such that every degenerate weakly ($k_1$, $k_2$)-quasiregular mapping f ${in}$ $W_{loc}^{1,q_1}$ (${Omega}$, $R^n$) belongs to $W_{loc}^{1,p_1}$ (${Omega}$, $R^m$), that is, f is a degenerate ($k_1$, $k_2$)-quasiregular mapping in the usual sense.