NOVELTY - A water-system suspension or hydrated compound comprising lithium manganese iron phosphate obtained by hydrothermal treatment, 60 wt.% or more lithium compound and/or phosphorus compound (I) and 1-20 wt.% organic substance, and having lithium and phosphorus in the molar ratio of 0.98-1.2, calculated using specific relation, is produced. The water-system suspension or hydrated compound is dried to obtain a precursor mixed powder. The precursor mixed powder is baked to obtain a carbon composite lithium manganese iron phosphate particles powder of olivine type structure.    USE - Manufacture of carbon composite lithium manganese iron phosphate particles powder for positive electrode active material for nonaqueous electrolyte secondary batteries (all claimed) used for hybrid vehicles and electric vehicles. Uses include but are not limited to audio-video equipment, personal computer and cordless portable electric tool.    ADVANTAGE - The method enables environmentally-friendly manufacture of carbon composite lithium manganese iron phosphate particles powder having small electrical resistance, favorable crystallinity, favorable surface and particle diameter and excellent fillability, economically. The secondary battery containing carbon composite lithium manganese iron phosphate particles powder has excellent capacity even in electric current load characteristics at low temperature and cycle characteristics at high temperature.    DETAILED DESCRIPTION - A water-system suspension or a hydrated compound comprising lithium manganese iron phosphate obtained by hydrothermal treatment, 60 wt.% or more lithium compound and/or phosphorus compound of formula: Li1-yH2+yPO4 (I) and 1-20 wt.% organic substance, and having lithium and phosphorus in the molar ratio of 0.98-1.2, calculated using the relation: Li/(Mn+Fe), P/(Mn+Fe) and P is less than Li, is produced. The water-system suspension or hydrated compound is dried to obtain a precursor mixed powder. The precursor mixed powder is baked to obtain a carbon composite lithium manganese iron phosphate particles powder of olivine type structure. The carbon composite lithium manganese iron phosphate particles powder has a molar ratio of manganese and iron (Mn:Fe) of 0.98:0.02-0.5:0.5. The content of lithium compound and/or phosphorus compound and organic substance are with respect to lithium manganese iron phosphate.    y=0-1.