Optical manipulation of micro-particles with nondiffracting and self-accelerating beams has been successfully applied in many research fields such as chemicophysics, material sciences and biomedicine. Such operation mainly focuses on the particle transport and control in the beam propagation direction. However, the conventional optical microscopy is specifically designed for obtaining the sample information located in the lateral plane, which is perpendicular to the optical axis of the detecting objective lens, making the real-time observation of particle dynamics in axial plane a challenge. In this work, we propose and demonstrate a technique which integrates a special beam optical tweezer with a direct axial plane imaging system. Here, particles are transported in aqueous solution along a parabolic trajectory by a designed nonparaxial Weber self-accelerating beam, and the particle motion dynamics both in lateral and axial plane are monitored in real-time by the axial plane imaging technique.