The distance matrix of a simple graph G is D(G)=(^dij), where ^dij is the distance between ith and jth vertices of G. The spectrum of the distance matrix is known as the distance spectrum or D-spectrum of G. A simple connected graph G is called distance regular if it is regular, and if for any two vertices x,y ∈ G at distance i, there are constant number of neighbors ^ci and ^bi of y at distance i-1 and i+1 from x respectively. In this paper we prove that distance regular graphs with diameter d have at most d+1 distinct D-eigenvalues. We find an equitable partition and the corresponding quotient matrix of the distance regular graph which gives the distinct D-eigenvalues. We also prove that distance regular graphs satisfying ^bi=cd-1 have at most ⌈d/2⌉ +2 distinct D-eigenvalues. Applying these results we find the distance spectrum of some distance regular graphs including the well known Johnson graphs. Finally we also answer the questions asked by Lin et al. [16].