Piezoelectric energy harvesting technology using flow-induced vibration is a type of interference-resistant and miniaturizable power generation technology, which is promising on powering the wireless micro electromechanical system (MEMS) in flow filed. However, the flow direction of the natural flow field is changeable while most existing flow-induced piezoelectric energy harvesters (PEHs) are limited by their working direction. In this paper, we propose a conical spiral piezoelectric energy harvester with parallel beams (CSPEH-PB) that can collect energy under flow excitation in all directions. Based on the multi-dimensional vibration analysis of conical spiral structure, we establish the dynamic model of the CSPEH-PB and investigate the differences between the CSPEH-PB and PEH with straight beam on the resonance bandwidth and effective flow velocity range through modal simulation. In comparative experiments with a bimorph flat PEH, we verify the effective flow velocity range and voltage of the CSPEH-PB and PVDF films attached. The results demonstrate that the CSPEH-PB generates an effective voltage greater than 0.53 V through the PVDF films under any direction of the water flow, and has a wider resonance bandwidth than PEH with straight beam. This study provides a practical solution for adapting PEHs to changeable flow direction.