Unpredictable random numbers is the key to ensure the security of quantum communication. We discuss the multi-bit random number produced by the evolution of a quantum walk via the single-bit input, the preparation of multi-path coherent superposition state, and single quantum measurement. We have investigated in detail the influences of input state, precisely engineered evolution and number of evolution steps on the randomness of multi-bit quantum pure states. As for the current single-photon detection technology, quantum walks provide a good platform to increase the generation rate of random numbers.