In this paper, based on the transfer function bounding techniques for turbo codes, we propose performance bounds on turbo coded hybrid automatic repeat request (TC-HARQ) under additive white Gaussian noise (AWGN) channel. The bounds for both Type-I TC-HARQ and segment selective repeat (SSR)-based TC-HARQ are developed in terms of bit error rate (BER), frame error rate (FER), and throughput. The performance predicted by these bounds are compared with simulation results and show close match in high signal to noise ratio (SNR) regions. The proposed bounds therefore provide good estimates on the error correction performance of TC-HARQ in high SNR regions where simulations are difficult to obtain reasonable results.