We propose a new Bayesian Markov chain Monte Carlo algorithm for continuous time GARCH diffusion limit stochastic volatility models and demonstrate the performance of our algorithm through simulation experiments and empirical analyses. Our algorithm exploits the normal distribution approximation of the posterior density of conditional variance using the one-step Newton- Raphson algorithm. Our algorithm can be applied not only to the continuous time GARCH diffusion limit stochastic volatility model but also to the continuous time stochastic volatility models of which the marginal probability density functions or the probability kernels of them are known. We present an empirical analysis results of the Feller square-root stochastic volatility model as well as the continuous time GARCH diffusion limit stochastic volatility model as an exhibition of the generality of our MCMC algorithm.