This work presents a bio-medical amplifier with programmable Gain and Bandwidth. The bandwidth of the proposed amplifier is controlled by tuning the unity-gain bandwidth (UGBW) of a rail-to-rail CMOS operational amplifier. The amplifier gain is controlled by changing the input capacitors keeping the bandwidth unchanged. The proposed bio-medical amplifier capable to accommodate different signals with a bandwidth ranging from 50 Hz up to 10 kHz to detect different bio-potential signals: EEG, ECG, EMG, PCG, and Aps, using fixed and small load capacitance. The proposed bio-medical amplifier consists of two stages each one designed with Tera ohm CMOS pseudo-resistors used in the amplifier feedback. The lower cutoff frequency of the bio-medical amplifier is tuned using two biasing currents in the CMOS pseudo-resistors, while two biasing voltages in the CMOS op-amps tune the higher cutoff frequency. The gain of the proposed bio-medical amplifier is ranging from 44.3 dB to 65.1 dB. High stability of the CMOS based op-amps (phase margin ≥60°) over the whole Gain and Bandwidth ranges is achieved. The overall power consumption of the bio-medical amplifier is less than 3.28 μW at the maximum gain settings of 65 dB and a maximum bandwidth of 10 k Hz. The total harmonic distortion of the proposed amplifier less than 1.21% for an input amplitude of 1 mVpk-pk over the entire bandwidth. The Input referred noise spectral density is 426 nV/Hz @1 kHz for the maximum bandwidth settings. The proposed bio-medical amplifier achieves an IIP3 value of 19.44 dBm for the amplifier gain of 54.9 dB. The simulation results show that the proposed bio-medical amplifier is robust against the PVT variations. LT-spice simulations using the standard 90 nm CMOS technology under 1 V supply voltage are performed to validate the theoretical results of the proposed amplifier.