In previous studies, the receivers in indoor visible light communication (VLC) were usually fixed. However, in reality, the receivers in VLC have random locations and orientations. Therefore, it is important to consider these random factors for performance analysis in VLC. In this paper, we consider a typical VLC system with a fixed transmitter and a random receiver. Two types of receivers are investigated: (1) those with random location and (2) those with random orientation. Based on the established system model, the statistical characteristics of the channel were obtained, and closed-form expressions of the average channel capacity and the outage probability were derived, respectively. Finally, numerical results verified the accuracy of derived theoretical expressions. Moreover, the effects of the nominal optical intensity, the dimming target, the transmitter height, the receiver zone's radius, the outage threshold, and the Lambertian emission order on system performance were also provided.