Many shortcomings of chaos-based applications stem from the weak dynamic properties of the chaotic maps they use. To alleviate this problem, inspired by the buffeting effect in aeroelasticity, this article proposes the buffeting chaotification model (BCM). Using the especially designed buffeting and modulo operators, the BCM can generate numerous new chaotic maps with strong dynamic properties from existing one-dimensional chaotic maps. The effectiveness of the BCM is mathematically proven according to the Lyapunov exponent, and further numerical experiments confirm the superiority of the chaotic maps generated by the BCM in terms of the dynamic properties. The field-programmable gate array implementation also shows that the BCM owns simplicity in hardware devices. To investigate the practical application, a scheme for constructing the pseudorandom number generator is designed. Performance analyses indicate that our generators have a strong ability to produce high-quality pseudorandom sequences rapidly.