Independent vector analysis (IVA) has exhibited great potential for the group analysis of magnitude-only fMRI data, but has rarely been applied to native complex-valued fMRI data. We propose an adaptive fixed-point IVA algorithm by taking into account the extremely noisy nature, large variability of the source component vector (SCV) distribution, and non-circularity of the complex-valued fMRI data. The multivariate generalized Gaussian distribution (MGGD) is exploited to match the SCV distribution based on nonlinearity, the shape parameter of MGGD is estimated using maximum likelihood estimation, and the nonlinearity is updated in the dominant SCV subspace to achieve denoising goal. In addition, the pseudo-covariance matrix is incorporated into the algorithm to represent the non-circularity. Experimental results from simulated and actual fMRI data demonstrate significant improvements of our algorithm over a complex-valued IVA-G algorithm and several circular and noncircular fixed-point IVA variants.