For model privacy, local model parameters in federated learning shall be obfuscated before sent to the remote aggregator. This technique is referred to as emph{secure aggregation}. However, secure aggregation makes model poisoning attacks such backdooring more convenient considering that existing anomaly detection methods mostly require access to plaintext local models. This paper proposes SAFELearning which supports backdoor detection for secure aggregation. We achieve this through two new primitives - emph{oblivious random grouping (ORG)} and emph{partial parameter disclosure (PPD)}. ORG partitions participants into one-time random subgroups with group configurations oblivious to participants; PPD allows secure partial disclosure of aggregated subgroup models for anomaly detection without leaking individual model privacy. SAFELearning can significantly reduce backdoor model accuracy without jeopardizing the main task accuracy under common backdoor strategies. Extensive experiments show SAFELearning is robust against malicious and faulty participants, whilst being more efficient than the state-of-art secure aggregation protocol in terms of both communication and computation costs.