In this paper, an asymmetric coupled map lattice (CML) combining sawtooth map as a local map is presented and its chaotic behaviours are analysed. Based on this asymmetric CML, a pseudorandom bit generator (PRBG) is proposed. The specific parameters of the system that make complicated floating-point computation and multiplication computation transform into simple shift bit operations are adopted, that not only ensures the nonlinear operations, but also increases the performance efficiency. The PRBG is implemented in software and hardware. The parallel output bit sequences pass all of the NIST SP800-22 statistical tests.