We have done the microscopic study of neutron-rich odd-odd iodine isotopes within the framework of projected shell model. Odd-odd nuclei are the best candidates for studying possible structure variations away from the valley of stability. We used the projected shell model, in which the deformed Nilsson single-particle states are being used for the construction of model basis. We studied the band properties of odd-odd I[Formula: see text](Z [Formula: see text] 53) isotopes with neutron numbers N [Formula: see text] 75, 77, 79, 81, 83 and 85. Using model analysis, we presented the low-lying positive- and negative-parity states of these nuclei. In these isotopes, the band structures have been analyzed in terms of quasi-particle configurations and comparative presentation of yrast levels is discussed. The phenomenon of yrast energy splitting is also studied in this work.