Implied volatilities are more efficient in the long-term prediction of volatilities than the series models. Solving the implied volatility is a typical PDE inverse problem. The traditional Tikhonov regularization method may over-smooth the solution. Considering the jump, overnight, weed-end effect of the volatility and the advantage of the total variation regularization which preserve the edge of the restored image, we put the problem of determining the implied volatility into a parabolic equation of the terminal problem under the Black-Scholes theoretical framework, propose the total variation regularization method and prove the existence to the solution.