We propose and experimentally demonstrated an all-optical radio-frequency (RF) spectrum analyzer, based on asynchronous optical sampling (ASOPS) assisted temporal convolution. The RF spectrum is mapped onto the time axis with the help of the temporal convolution system. In combination with the bandwidth compression capability of the ASOPS scheme, up to 28-GHz RF spectrum can be directly read out by an acquisition system with bandwidth as low as 20 MHz. The experimental results demonstrated about 100-MHz resolution and 28-GHz observation bandwidth. The resolution can be improved by increasing the amount of temporal dispersion or optical spectral bandwidth, and the bandwidth can be further extended by compensating the higher-order dispersion, although it is currently mainly limited by that of the electro-optic modulator. The frame rate is flexibly tunable by changing the repetition rate difference between the two mode-locked fiber lasers. Moreover, nearly 25-dB dynamic range indicates this system has a promising application prospect.