Synthetic carbon-coated olivine-like structured lithium iron phosphate ($Li^+Fe^{2+}(PO_4)^{3-}/C$) powder composites were compressed up to 35.0 GPa in the symmetrical diamond anvil cell at room temperature. Bulk modulus of $LiFePO_4/C$ was determined to be $130.1{pm}10.3$ GPa. New peak appears at the d-spacing of 3.386 ${AA}$ above 18 GPa, and another new one at 2.854 ${AA}$ around 35 GPa. The crystallographic symmetry of the sample (i.e. orthorhombic) is apparently retained up to 35 GPa as no clear evidence for the phase transition into spinel structure has been observed. The pressure-induced volume change in the M1 site ($Li^+O_6$) is more significant than those in M2($Fe^{2+}O_6$) and $PO_4$ tetrahedral sites.