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The entanglement distribution network connects remote users through sharing entanglement resources, which is essential for realizing quantum internet. We proposed a controllable entanglement distribution network (c-EDN) based on a silicon quantum photonic chip. The entanglement resources were generated by a quantum light source array based on spontaneous four-wave mixing (SFWM) in silicon waveguides and distributed to different users through time-reversed Hong-Ou-Mandel interferences in on-chip Mach-Zehnder interferometers with thermal phase shifters. A chip sample was designed and fabricated, supporting a c-EDN with 3 subnets and 24 users. The network topology of entanglement distributions could be reconfigured in three network states by controlling the quantum interferences through the phase shifters, which was demonstrated experimentally. Furthermore, a reconfigurable entanglement-based QKD network was realized as an application of the c-EDN. The reconfigurable network topology makes the c-EDN suitable for future quantum networks requiring complicated network control and management. Moreover, it is also shows that silicon quantum photonic chips have great potential for large-scale c-EDN, thanks to their capacities on generating and manipulating plenty of entanglement resources.