We developed an electron-counting technique for a self-referenced single-electron quantized current source of a single-electron-pump system and investigated the fidelity of our whole measurement process, including single-electron pumping and electron counting by a single-electron transistor (SET) with a charge-lock feedback loop. The device was fabricated monolithically using a two-dimensional electron system of a GaAs/AlGaAs hetero-junction. In addition to the probability of single-electron transfer, we also measured the current noise spectrum of the SET, from which its charge noise power [Formula: see text] was derived. The results show that the estimated charge noise of 2.2 [Formula: see text] for a semiconductor-based SET is comparable to that of metallic SETs.