The required testing duration of software reliability demonstration testing (SRDT) for the continuous safety-critical software is generally too long to endure. To solve this problem, a new continuous Bayesian-based SRDT scheme (CBSDF) for the safety-critical software is proposed by using the decreasing function method with the prior information. The representative decreasing function of the continuous reliability index (such as the failure rate) is selected to construct the prior distribution density function (PDDF). Then, the estimation values of the hyper-parameters of PDDF are calculated according to the prior information (i.e. the failure data collected in reliability growth testing) to obtain the posterior distribution and the detailed form of CBSDF. By selecting two failure data-sets as the source of prior information, the proposed CBSDF is compared with two existing Bayesian-based schemes (i.e. CBS1 without prior information and CBS2 with prior information). The experimental results show that with the same given reliability index, the proposed CBSDF is more effective than CBS1 and CBS2 by significantly decreasing the required testing time of SRDT and more suitable for the safety-critical software with high reliability.