Deemed as a practical approach to realize Visible Light Communication on commercial-off-the-shelf devices, the Optical Camera Communication (OCC) is attracting increasing attention, thanks to its readiness to be built purely upon ubiquitous LED illuminating infrastructure and handy smartphones. However, limited by the low sampling ability of the built-in camera on a smartphone, the performance of existing OCC systems is still far away from the requirements of practical applications. To this end, we further investigate the reception ability of the smartphone's camera and propose an accumulative sampling scheme to improve the performance of the OCC system. Essentially, the proposed scheme can use all the grayscale information of the pixels projected by the LED transmitter, whereas the conventional ones normally use single row (or column) pixels for demodulating. By implementing the lightweight demodulation algorithm with accumulative sampling, we experimentally verify its effectiveness for supporting higher transmission frequency hence better performance in terms of data rate. Extensive evaluations have shown the BERs of the proposed method are over 87% and 96% lower than that provided by the baselines at a maximum transmission frequency of 5 kHz for the Samsung S8 and iPhone 8 Plus receivers, respectively.