This paper presents a novel axisymmetric floating energy harvester associated with hydraulic cylinders and gear rack mechanism to harness wave energy. The harvester collects energy in surge, heave, and pitch modes. The mathematical models for the harvester are developed to analyze the performance and the harvested power. The Pierson-Moskowitz two-parameter spectrum was utilized to model the incident waves. The retardation function for the radiation force and the added mass curve are fitted based on the least squares method. The irregular exciting force, the displacement, the velocity, and the power harvesting of the axisymmetric floating energy harvesters in three motion modes with irregular waves are simulated. The effects of harvester design parameters and the geometry shape variation of the submerged part on the wave-exciting force, the displacement, the velocity, the harvested power, and the harvesting efficiency are investigated. Under the same output damping and the same parameters with the radius of 4 m, the submerged height of 4 m, the above-water height of 2 m, and the center of mass of -1 m, the cylinder wave-exciting force in surge is highest among three shapes, the cone wave-exciting force is highest among three shapes in heave and pitch modes, and the total harvested power and the efficiency of the cylinder-shaped harvester are the highest among three different axisymmetric shapes, which are 40.521 kW and 62.96%, respectively. The harvested power and the efficiency differences between the cylinder and the cone are 1.571 kW and 2.4%, and the differences between the cylinder and the halfsphere are 8.543 kW and 13.28%. For the cylinder-shaped harvester with the submerged height of 4 m, the above-water height of 2 m, and the center of mass of -1 m, when the radius increases from 3 m to 5 m, under the optimal output damping, the total harvested power and the harvesting efficiency increase by 38.811 kW and 35.83%, respectively. For the cylinder-shaped harvester with the radius of 4 m and the above-water height of 2 m, as the submerged part height increases from 2 to 4 m, the total harvested power and the harvesting efficiency increase by 15.776 kW and 24.51%, respectively. For the cylinder-shaped harvester with the radius of 4 m, the submerged height of 4 m, and the above-water height of 2 m, as the center of mass is reduced from 0 to -1 m, the total harvested power and the harvesting efficiency rise by 15.153 kW and 23.54%, respectively.