Quantum key distribution (QKD) technology provides proven unconditional point-to-point security based on fundamental quantum physics. A QKD network also holds promise for secure multi-user communications over long distances at high-speed transmission rates. Although many schemes have been proposed so far, the trusted relay QKD network is still the most practical and flexible scenario. In reality, the insecurity of certain relay sections cannot be ignored, so to solve the fatal security problems of partially-trusted relay networks we suggest a multiple stochastic paths scheme. Its features are: (i) a safe probability model that may be more practical for real applications; (ii) a multi-path scheme with an upper bound for the overall safe probability; (iii) an adaptive stochastic routing algorithm to generate sufficient different paths and hidden routes. Simulation results for a typical partially-trusted relay QKD network show that this generalized scheme is effective. AQKD network also holds promise for secure multi-user communications over long distances at high-speed transmission rates. Although many of the schemes have been proposed so far, the trusted relay QKD network is still the most practical and flexible scenario. In reality, the insecurity of certain relay sections can not be ignored, so to solve the fatal security problems of partially-trusted relay networks we suggest a multiple stochastic paths scheme Its features are: (i) a safe probability model that may be more practical for real applications; (ii) a multi-path scheme with an upper bound for the overall safe probability; (iii) an adaptive stochastic routing algorithm to generate sufficient different paths and hidden routes. Simulation results for a typical partially-trusted relay QKD network show that this generalized scheme is effective.