In this paper, we investigate the problem of recovering positive semi-definite (PSD) matrix from 1-bit sensing. The measurement matrix is rank-1 and constructed by the outer product of a pair of vectors, whose entries are independent and identically distributed (i.i.d.) Gaussian variables. The recovery problem is solved in closed form through a convex programming. Our analysis reveals that the solution is biased in general. However, in case of error-free measurement, we find that for rank-r PSD matrix with bounded condition number, the bias decreases with an order of O(1/r). Therefore, an approximate recovery is still possible. Numerical experiments are conducted to verify our analysis.