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Integrated photonics provides a versatile platform for encoding and processing quantum information. However, the encoded quantum states are sensitive to noise, which limits their capability to perform complicated quantum computations. Here, we use a five-qubit linear cluster state on a silicon photonic chip to implement a quantum error-correction code and demonstrate its capability of identifying and correcting a single-qubit error. The encoded quantum information is reconstructed from a single-qubit error and an average state fidelity of 0.863±0.032 is achieved for different input states. We further extend the scheme to demonstrate a fault-tolerant measurement-based quantum computation (MBQC) on stabilizer formalism that allows us to redo the qubit operation against the failure of the teleportation process. Our work provides a proof-of-concept working prototype of error correction and MBQC in an integrated photonic chip.