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Independent vector analysis (IVA) utilizing Gaussian mixture model (GMM) as source priors has been demonstrated as an effective algorithm for joint blind source separation (JBSS). However, an extra pre-training process is required to provide initial parameter values for successful speech separation. In this paper, we introduce a time-varying parameter in the GMM to adapt to the temporal power fluctuation embedded in the nonstationary speech signal so as to avoid the pre-training process. The expectation-maximization (EM) process updating both the demixing matrix and the signal model is altered correspondingly. Experimental results confirm the efficacy of the proposed method under random initialization and further show its advantage in terms of a competitive separation accuracy and a faster convergence speed.