Massive MIMO is a promising technique to provide unprecedented spectral efficiency. However, it has been well recognized that huge training overhead for obtaining channel side information (CSI) is a major handicap in frequency-division duplexing (FDD) massive MIMO. Several attempts have been made to reduce this training overhead by exploiting sparse structures of massive MIMO channels. So far, however, there has been little discussion about how to utilize partial support information of sparse channels to achieve further overhead reduction. This support information, which is a set of indexes of significant elements of a channel vector, actually can be acquired in advance. In this paper, we examine the required training overhead when partial support information is applied within a weighted ℓ1 minimization framework and analytically show that a sharp estimate of this overhead size can be successfully obtained. Furthermore, we demonstrate that the accuracy of partial support information plays an important role in determining how much reduction can be achieved. Numerical results shall verify the main conclusions.