Ternary iron phosphide EuFe$_2$P$_2$ with ThCr$_2$Si$_2$-type structure has been systematically studied by the measurements of crystal structure, magnetization, M{o}ssbauer effect, transport properties and specific heat. The structural refinement result confirms no direct P-P covalent bonding. The M{o}ssbauer spectra indicate no magnetic moment for the Fe atoms and, that the Eu ions are divalent in the whole temperatures, carrying local moments of $S$=7/2. The Eu$^{2+}$ spins order ferromagnetically at $T_C$=29.5 K, followed by a possible helimagnetic ordering below $T_{HM}$=26 K, where the Eu$^{2+}$ moments tilt a little from the c-axis. External magnetic field increases $T_C$ gradually, but suppresses $T_{HM}$ rapidly. (Magneto)resistivity data indicate characteristic dense Kondo behaviour above the Curie temperature. The result is discussed in terms of the interplay between intersite RKKY and intrasite Kondo interactions.