In this paper, we describe the design, development and experimental results of a 3-DOF precise inchworm mechanism with six contact points. During the last ten years, we have developed an omnidirectional and holonomic inchworm mechanism to provide flexible, compact, and precise microscopic processing. In a previous mechanism, four piezoelectric actuators connected a pair of U-shaped electromagnets arranged to cross each other so that the mechanism can move precisely in any direction. However, positioning repeatability was made difficult by an inclination of the U-shaped electromagnets. Therefore, we designed a new omnidirectional inchworm mechanism composed of a pair of Y-shaped electromagnets and six piezoelectric actuators to prevent the inclination of the electromagnets. In addition, we explain the drive principle of the newly developed mechanism. Finally, we show the experimental results of the positioning repeatability of translational motions in four directions with a payload.