The complexity of the erbium doped fiber ring lasers is experimentally investigated based on the autocorrelation function and permutation entropy function. By controlling the loss in the ring cavity, the different chaotic complexity is analyzed in detail. The experimental results show that the intra-cavity loss has great effect on the chaotic complexity of fiber laser. With increase of the loss, the permutation entropy complexity increases gradually and the time- delay signature shown in the autocorrelation curves can also be suppressed. By controlling the intra-cavity loss, the time-delay signature of chaos is completely hidden and its permutation entropy complexity reaches a maximum, which can effectively improve the security of chaotic secure communications and the measurement precision of chaotic sensing or ranging.