This technical note is concerned with the stability problem of stochastic delayed systems by using a more general Halanay-type inequality with time-varying coefficients. A new comparison principle of the proposed Halanay-type inequality is developed to ensure the stability of stochastic delayed systems. The pth moment stability, pth moment asymptotic stability and pth moment exponential stability are investigated by means of the proposed general Halanay-type inequality. Two examples including one of the consensus of multi-agent systems with time-varying topologies and transmission delays are presented to demonstrate the effectiveness of the proposed results.