This book constitutes the refereed proceedings of the 9th International Conference on Theory and Practice of Natural Computing, TPNC 2020, held in Taoyuan, Taiwan, in December 2020. The 12 full papers presented in this book, together with one invited talk, were carefully reviewed and selected from 24 submissions. The papers are organized in topical sections named: applications of natural computing; quantum computing and unconventional computing; and swarm intelligence, evolutionary algorithms, and DNA computing.