We propose a Leaky Integrate-and-Fire neuron circuit with a long and tunable time constant. The proposed circuit consists of an amplifier with a capacitor and two pseudo resistors (PRs). Thanks to the property of PR that realizes high resistance only with 4 MOS FETs, we can emulate a long time constant of synaptic integration with small on-chip capacitor, which leads to small occupation area. We can tune the time constant by changing the resistance of the PR with external bias voltage. Implemented in 65nm CMOS, the maximum time constant of 0.15ms is achieved with 2pF on-chip capacitance.