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In this paper we show how to derive the Bogomolny's equations of thegeneralized self-dual Maxwell-Chern-Simons-Higgs model presented in\cite{Bazeia:2012ux} by using the BPS Lagrangian method with a particularchoice of the BPS Lagrangian density. We also show that the identification,potential terms, and Gauss's law constraint can be derived rigorously under theBPS Lagrangian method. In this method, we find that the potential terms are themost general form that could have the BPS vortex solutions. The Gauss's lawconstraint turns out to be the Euler-Lagrange equations of the BPS Lagrangiandensity. We also find another BPS vortex solutions by taking otheridentification between the neutral scalar field and the electric scalarpotential field, $N=\pm A_0$, which is different by a relative sign to theidentification in \cite{Bazeia:2012ux}, $N=\mp A_0$. Under this identification,$N=\pm A_0$, we obtain a slightly different potential terms and Bogomolny'sequations compared to the ones in \cite{Bazeia:2012ux}. Furthermore we computethe solutions numerically, with the same configurations as in\cite{Bazeia:2012ux}, and find that only the resulting electric field plotsdiffer by sign relative to the results in \cite{Bazeia:2012ux}. Therefore weconclude that these BPS vortices are electric-dual BPS vortices of the onescomputed in \cite{Bazeia:2012ux}.

Electric-dual BPS Vortices in The Generalized Self-dual Maxwell-Chern-Simons-Higgs Model