We propose a new approach to nondeterministic random number generation. In theory, the randomness originated from the uncorrelated nature of consecutive laser pulses with Poissonian photon number distribution and that of the consecutive single photon detections is used to generate random bit. In experiment, von Neumann correction method is applied to extract the final random bit. This method is proved to be bias free in randomness generation, provided that the single photon detections are mutually independent, and further, it has the advantage in generation efficiency of random bits since no postprocessing is needed. A true random number generator based on this new method is realized and its randomness is guaranteed using three batteries of statistical tests.