An optimal reinsurance and investment problem with relative performance under stochastic volatility and default risk are investigated. Assume that proportional reinsurance is allowed and the surplus of the insurer can be allocated to the financial market consisting of the risk-free asset, the default bond and the risky asset whose price process satisfies square root factor process. Particularly, the delay of feedback time is taken into account. Then based on the approach of stochastic control, closed-form expressions of the optimal strategies and the corresponding value functions are derived. Finally, numerical experiments are provided to illustrate how the model parameters affect optimal strategies. Besides, optimal strategies under different objective criteria are compared to further reveal the parameters influences.