The charge-integration readout circuit was fabricated to achieve an ultralow-noise preamplifier for photoelectrons generated in an avalanche photodiode with linear mode operation at 77 K. To reduce the various kinds of noise, the capacitive transimpedance amplifier was used and consisted of low-capacitance circuit elements that were cooled with liquid nitrogen. As a result, the readout noise is equal to 3.0 electrons averaged for a period of 40 ms. We discuss the requirements for avalanche photodiodes to achieve photon-number-resolving detectors below this noise level.