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We minimally coupled a scalar potential $V(\phi)$ with asymmetric vacua tothe Einstein gravity to numerically construct the hairy Reissner-Nordstromblack hole (RNBH) as a direct generalization of RNBHs to possess scalar hair.By fixing the electric charge to mass ratio $q$, a branch of hairy RNBHsbifurcates from the RNBH when the scalar field $\phi_H$ is non-trivial at thehorizon. The values of $q$ are bounded for $0 \leq q \leq 1$, which contrast toa class of hairy black holes with $q>1$ in the Einstein-Maxwell-scalar theory.We find that the profiles of solutions affected by the competition between thestrength of $\phi_H$ and $q$, for instance, the gradient of scalar field at thehorizon can increase very sharply when $q \rightarrow 1$ and $\phi_H$ is smallbut its gradient can be very small which independent of $q$ when $\phi_H$ islarge. Furthermore, the weak energy condition of hairy RNBHs, particularly atthe horizon can be satisfied when $q>0$.

Hairy Reissner-Nordstrom Black Holes with Asymmetric Vacua