The invention relates to a lithium-transition metal compound powder for a positive-electrode material for lithium secondary battery which comprises secondary particles configured of primary particles having two or more compositions and a lithium-transition metal compound having a function of being capable of insertion and release of lithium ions, wherein the powder gives a pore distribution curve having a peak at a pore radium 80 nm or greater but less than 800 nm, and the secondary particles include primary particles of a compound represented by a structural formula including at least one element selected from As, Ge, P, Pb, Sb, Si and Sn, wherein the primary particles of the compound are present at least in an inner part of the secondary particles.