The invention provides a spherical supported type non-metallocene transition metal catalyst. According to the spherical supported type non-metallocene transition metal catalyst, a spherical titanium/zirconium hydrogen phosphate compound serves as a carrier, a non-metallocene transition metal compound serves as a main catalyst, and methylaluminoxane serves as a catalyst promoter. The spherical titanium/zirconium hydrogen phosphate compound comprises one or a combination of titanium hydrogen phosphate, modified titanium hydrogen phosphate and zirconium hydrogen phosphate. The invention further provides a preparation method of the spherical supported type non-metallocene transition metal catalyst and application of the spherical supported type non-metallocene transition metal catalyst in olefin polymerization as well as the spherical titanium/zirconium hydrogen phosphate compound and a preparation method thereof. The spherical supported type non-metallocene transition metal catalyst provided by the invention has high catalytic activity and obtained polymer particles are good in morphology.