Pound-Drever-Hall (PDH) laser frequency stabilization is a powerful technique widely used for building narrow-linewidth lasers. This technique is however ineffective in suppressing high-frequency (>100~kHz) laser phase noise detrimental for many applications. Here, we introduce an effective method which can greatly enhance its high-frequency performance. The idea is to recycle the residual PDH signal of a laser locked to a cavity, by feedforwarding it directly to the laser output field after a delay fiber. Using this straightforward method, we demonstrate a phase noise suppression capability about 4 orders of magnitude better than just using usual PDH feedback for phase noise around a few MHz. We further find that this method exhibits noise suppression performance equivalent to cavity filtering. The new method holds great promise for applications demanding highly stable lasers with diminished phase noise up to tens of MHz, e.g. precise and high-speed control of atomic and molecular quantum states.