NOVELTY - A solution (S1) containing lithium and phosphorus is prepared (S111-1). A solution (S2) containing transition metal(s) chosen from iron, cobalt, nickel and manganese is prepared (S111-2). The obtained solutions (S1) and (S2) are mixed (S113) to obtain mixture solution. The obtained mixture solution is subjected to hydrothermal process (A) (S114) to obtain lithium-transition metal phosphate (I). All reactions are carried out under an atmosphere (A1) where concentration of oxygen is lower than in air.    USE - Manufacture of lithium-transition metal phosphate used for power storage device (claimed). Uses include but are not limited to electric vehicle, hybrid vehicle, electric motor, motorized bicycle, liquid crystal display device, digital micromiror device, plasma display panel, field emission display, personal computer, television etc.    ADVANTAGE - The method enables uniform-sized, cube-shaped lithium-transition metal phosphate with suppressed generation of by-products.    DETAILED DESCRIPTION - A solution containing lithium and phosphorus is prepared. A solution containing transition metal(s) chosen from iron, cobalt, nickel and manganese is prepared. The obtained two solutions are mixed to obtained mixture solution. The obtained mixture solution is subjected to hydrothermal process to obtain lithium-transition metal phosphate of formula: LiMPO4 (I). All reactions are carried out under an atmosphere (A1) where concentration of oxygen is lower than in air.    M=Fe, Co, Ni or Mn.    An INDEPENDENT CLAIM is included for manufacture of power storage device, which consists of a positive electrode formed using the lithium-transition metal phosphate (I).    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic view explaining manufacture of lithium-transition metal phosphate.    Process of weighing lithium-phosphorus compound (S111-1)    Process of forming solution containing lithium and phosphorus (S112-1)    Process of forming solution containing transition metal (S112-2)    Process of forming mixture solution (S113)    Process of forming lithium-transition metal phosphate by hydrothermal process (S114)