  We study the electronic instabilities of newly predicted Ni-based high-$T_c$
superconducting material La$_2$Ni$_2$Se$_2$O$_3$ based on the random phase
approximation. Our calculations on the susceptibility indicate that the
collinear antiferromagnetic state in the parental compound is induced by the
perfect Fermi surface nesting. Our further calculations reveal that the ground
states of the doped compound are the $s_{\pm}$- and $d_{xy}$-wave
superconducting states driven by the antiferromagnetic spin fluctuations
enhanced by the quasi-nestings. Interestingly, the $s$- and $d$-wave pairings
occur in the hole and electron doping cases, respectively. This doping-type
dependence of the pairing symmetry can be understood from the doping dependence
of the nested Fermi pockets.
