A Bloch point (BP) is, as far as we know, the only magnetization singularity in a ferromagnet at which the local magnetization vanishes. Around the BP, magnetizations are formed the unique topological structure having an integer topological number. In nanomagnetic systems, BPs bear critical roles in many dynamical phenomena of spin structures. In general, BPs should be mediated to achieve a change in the topological numbers in spin structures. For example, the switching of magnetic vortex core, which implies the change of the topological number from +1/2 to -1/2 or vice versa, is accomplished through the injection and propagation of the BPs [1-3]. Besides such a vital role in the switching dynamics, it has atomistic nature since the virtual magnetizationvanishing point should be located in the middle of the lattice point. To observe such intrinsic natures of BP, it is indispensable to form a BP in magnetic nanostructures. In this presentation, we report experimental observation of steady-state BPs in the middle of elongated magnetic vortex cores in asymmetrically shaped Permalloy nanodisks [4] by using the magnetic transmission soft X-ray microscopy (MTXM) at the Advanced Light Source [5]. From time-resolved nanoscale magnetic X-ray imaging combined with micromagnetic simulations, detailed dynamic character of BPs, revealing rigid and limited lateral movements under magnetic field pulses as well as its crucial role in vortex-core dynamics.