Owing to the property of elastic wave band gap, the piezoelectric phononic crystals have been used for noise and vibration control. In this paper, a piezoelectric phononic crystal rod structure is constructed by periodically arranging a piezoelectric shunt unit with negative capacitance on the epoxy resin rod. In order to expand the wide band gap, three cell configurations are designed for this structure, the transfer matrix method is used to calculate the band gap characteristics, and the genetic algorithm is used to optimize the shunt circuit parameters. The theoretical and simulation results show that by changing the number of piezoelectric shunt units with different resonance frequencies in the cell, multiple local resonance band gaps can be obtained, and the band gap tunability can be enhanced. By using the algorithm optimization, the best matching of the shunt circuit parameters can be obtained when the band gap is tuned, and the combination of multiple bandgaps can be realized and the wide band gap can be expanded without changing the original structure.