Visible light communication (VLC) has attracted much attention in the research of sixth-generation (6G) systems. Furthermore, channel modeling is the foundation for designing efficient and robust VLC systems. In this paper, we present extensive VLC channel measurement campaigns in indoor environments, i.e., an office and a corridor. Based on the measured data, the large-scale fading characteristics and multipath-related characteristics, including omnidirectional optical path loss (OPL), K-factor, power angular spectrum (PAS), angle spread (AS), and clustering characteristics, are analyzed and modeled through a statistical method. Based on the extracted statistics of the above-mentioned channel characteristics, we propose a statistical spatial channel model (SSCM) capable of modeling multipath in the spatial domain. Furthermore, the simulated statistics of the proposed model are compared with the measured statistics. For instance, in the office, the simulated path loss exponent (PLE) and the measured PLE are 1.96 and 1.97, respectively. And, the simulated medians of AS and measured medians of AS are 25.94° and 24.84°, respectively. Generally, the fact that the simulated results fit well with measured results has demonstrated the accuracy of our SSCM.