We report on the experimental observation of the proximity induced superconductivity in an indium gallium arsenide (In0.75Ga0.25As) quantum well. The Josephson junction was fabricated by several photo-lithographic processes on an InGaAs heterojunction and Niobium (Nb) was used as superconducting electrodes. Owing to the Andreev reflections and Andreev bound states at the Nb-In0.75Ga0.25As quantum well-Nb interfaces, the subharmonic energy gap structures (SGS) are observed at the differential conductance (dI/dV) versus voltage (V) plots when the applied source-drain bias voltages satisfy the expression VSD = 2Δ/ne. The dI/dV as a function of applied magnetic field B shows a maximum at zero B which decreases by increasing B. When decreasing B to below ±0.4 T, a hysteresis and shift of the conductance maxima close to B = 0 T are observed. Our results help to pave the way to the development of integrated coherent quantum circuitry.