The magnetic transition and conducting behaviors of LaMn1-xCuxO3 (x=0.05, 0.1, 0.2, 0.3, 0.4) system have been systematically studied. The results show that very small amount of Cu-doping (x=0.05) into the anti-ferromagnetic LaMnO3 matrix induces strong ferromagnetic transition below about 157K. The Curie temperature decreases gradually with the increase of Cu-doping content, while the magnetization increases firstly and then decreases. In accordance with the magnetic properties, the electrical resistivity decreases at low dopant (x≤0.10) and then increases with the increase of Cu-doping content. All samples exhibit insulating conducting behavior in the whole temperature range: from a paramagnetic insulator to a ferromagnetic insulator. The conducting behavior of lower doped samples (x≤0.10) is well fitted by the Mott Variable Range Hopping (VRH) model,and then favors to the thermoactivation model when 0.10≤x≤0.40. With the increase of Cu-doping content, the influence of Cu ions on the double exchange interaction among the Mn-O-Mn chains and the magnetic structure results in that the eg electron transport obeys the domination of potential barrier in the VRH model at lower doping and then favors the domination of energy gap in the thermal activation model at higher doping contents.