Quantum random numbers have an incomparable advantage over pseudo-random numbers since randomness originates from intrinsic property of quantum mechanics. The generation rate and the security of quantum random numbers are two significant indicators of a quantum random number generator (QRNG) for practical applications. Here we propose a mutually testing source-device-independent QRNG by simultaneously measuring a pair of conjugate quadratures from two separate parts of an untrusted continuous-variable quantum state. The amounts of randomness of the quadratures can be mutually estimated by each other via entropic uncertainty principle. Instead of randomly toggling between the conjugate quadratures of one state for collecting different types of data, two quadratures can generate check data and raw bits simultaneously and continuously in this mutually testing manner, which enhances the equivalent generation rate of private random bits to around 6 Gbit/s with a 7.5 mW laser beam. Moreover, the overall security is also improved by adjusting the conditional min-entropy in real time according to the continually monitored fluctuations of the local oscillator and the randomly measured electronic noise of homodyne detectors.