This paper theoretically studies the performance of transmission control protocol (TCP) over visible light communications (VLC) networks when the automatic-repeat request, selective repeat (ARQ-SR) protocol is employed in the link layer. We analytically derive TCP throughput considering the impact of ARQ-SR parameters and different VLC physical factors, including inter-symbol interference (ISI), signal reflection and light power distribution. Numerical results show that TCP throughput is strongly dependent on the location of VLC user due to impacts of ISI and signal reflection. It is also seen that the use of ARQ-SR could significantly improve both the maximum value and the distribution of TCP throughput in the VLC network. Especially, with a proper selection of the number of re-transmissions by the ARQ-SR protocol, the dependence of TCP throughput on user location caused by ISI, light signal reflection and distribution could be effectively remedied.