We grew single crystals of RCoGe3 (R: La, Cc, Pr, and Nd) by the Bi-flux method, and studied the magnetic properties of PrCoGe3 and NdCoGe3 and the pressure-induced superconducting property of CeCoGe3. These compounds crystallize in a non-centrosymmetric tetragonal structure. PrCoGe3 and NdCoGe3 were found to be a paramagnet and an anti ferromagnet with the Neel temperature T-N = 3.8 K, respectively. Crystalline electric field (CEF) schemes were proposed for PrCoGe3 and NdCoGe3. The magnetic property of a pressure-induced superconductor CeCoGe3 is highly different from those of PrCoGe3 and NdCoGe3, or a similar pressure-induced superconductor CeIrSi3. This was discussed in connection with the superconductivity of CeCoGe3. We clarified the upper critical field H-c2 for H parallel to [001] and [100] by measuring the electrical resistivity under pressure P in magnetic fields: H-c2(0) similar or equal to 24T for H parallel to [001] and H-c2(0) similar or equal to 3.1 T for H parallel to [100] at 0 K at P = 7.1 GPa. A huge H-c2(0) value for H parallel to [001] is a combined phenomenon between the Rashba-type antisymmetric spin-orbit interaction and the electronic instability, as observed in CeIrSi3.