In this letter, constructions of sequences with perfect odd autocorrelation and sequence sets with zero odd correlation zone (ZOCZ) over the 8-QAM+ constellation are presented. Based on odd perfect ternary sequences, odd perfect sequences and ZOCZ sequence sets over the 8-QAM+ constellation are constructed by using shift vectors and mappings. These odd perfect sequences and ZOCZ sequence sets over 8-QAM+ constellation can be used in communication systems to achieve high transmission data rate (TDR) and low interference.