This paper proposes two methods for reconstructing current distributions from biomagnetic measurements. Both of these methods are based on estimating the source-current covariance matrix from the measured-data covariance matrix. One method is the reconstruction of average current intensity distributions. This method first estimates the source-current covariance matrix and, using its diagonal terms, it reconstructs current intensity distributions averaged over a certain time. Although the method does not reconstruct the orientation of each current element at each time instant, it can retrieve information regarding the current time-averaged intensity at each voxel location using extremely low SNR data. The second method is Wiener reconstruction using the estimated source-current covariance matrix. Unlike the first method, this Wiener reconstruction can provide a current distribution with its orientation at each time instant. Computer simulation shows that the Wiener method is less affected by the choice of the regularization parameter, resulting in a method that is more effective than the conventional minimum-norm method when the SNR of the measurement is low.