A mixed graph $\widetilde{G}$ is obtained by orienting some edges of $G$, where $G$ is the underlying graph of $\widetilde{G}$. The positive inertia index of $\widetilde{G}$ is the number of positive eigenvalues of the Hermitian adjacent matrix of $\widetilde{G}$, denoted by $p^+(\widetilde{G})$, and the negative inertia index of $\widetilde{G}$ is the number of negative eigenvalues of the Hermitian adjacent matrix of $\widetilde{G}$, denoted by $n^-(\widetilde{G})$. For a mixed graph $\widetilde{G}$, the dimension of cycle space, denoted by $c(\widetilde{G})$, and the matching number, denoted by $m(\widetilde{G})$, are defined to be the dimension of cycle space and the matching number of its underlying graph, respectively. \par The first result of this paper is that, for a mixed unicyclic graph $\widetilde{G}$, the pair $ (p^+(\widetilde{G}), n^-(\widetilde{G}))$ is one of the following: $$ (m(\widetilde{G})-1,m(\widetilde{G})-1),\quad (m(\widetilde{G}),m(\widetilde{G})),\quad (m(\widetilde{G})+1,m(\widetilde{G})),\quad (m(\widetilde{G}),m(\widetilde{G})+1). $$ \par The second one is that, for a mixed graph $\widetilde{G}$, $$ m(\widetilde{G})-c(\widetilde{G})\leq p^+(\widetilde{G})\leq m(\widetilde{G})+c(\widetilde{G}) $$ and $$ m(\widetilde{G})-c(\widetilde{G})\leq n^-(\widetilde{G})\leq m(\widetilde{G})+c(\widetilde{G}). $$ The mixed graphs that attain the upper and lower bounds are characterized, respectively.