We propose ZigZag decodable coded slotted ALOHA (ZDCSA) by applying ZigZag decoding (ZD) into ALOHA scheme with successive interference cancellation (SIC), namely coded ALOHA. It is known that the throughput performance of coded ALOHA schemes degrades when a channel traffic is high. ZD is able to suppress such throughput degradation by resolving collisions of two packets, where the colliding users are requested to retransmit their packets immediately in order to utilize ZD. In this paper, an optimization method to maximize the throughput performance of ZDCSA is also proposed. Through numerical analysis, it is shown that our proposed scheme succeeds in suppressing the throughput degradation in high traffic region and outperforms coded ALOHA schemes in terms of peak throughput performance in a practical situation e.g. a system consists of 103 users.