We propose an operator Hermite polynomial method, namely, we replace the arguments of the special function by quantum mechanical operators, and in this way we derive a binomial theorem involving Hermite polynomials and a negative-binomial theorem involving Laguerre polynomials. These two theorems will have essential applications in quantum optics calculations. This method is concise and helpful in deducing many operator identities, which may become a new branch in mathematical physics theory.