Thanks to the extensive researches on fluorescence probe including the invention of immunofluorescence and discovery of green fluoresence protein, fluorescence microscopy has been a popular instrument tool to understand properties organic and inorganic specimens. However, due to the diffraction limit, conventional fluorescence microscopy cannot discern details of specimen that are closer than half of wavelength of emission light. Recently, far-field fluorescence microscopy to overcome the diffraction limit has been extensively studied. For example, stimulated emission depletion microscopy (STED) exploits stimulated emission phenomenon of fluorescence material to design sharp effective point spread function (PSF), by suppressing the rim of excitation spot. Saturated structure illumination microscopy (SSIM) can unlock the diffraction limit by high power parallel line pattern illumination which drops high order frequency components onto range of optical transfer function (OTF) as the similar way of structured illumination microscopy (SIM). In single molecule based approach such as STORM and PALM/FPALM, photoswitchable fluorescence molecule is used for super resolution localization. However, all these super resolution techniques have their own limit such as requirement of high power laser and massive hardware setup or specific photoswitchable dye. Here, we propose a novel 3D multi-color super resolution microscopy, called nanometer resolution imaging method using speckle illumination and multiple signal classification (Nano-MUSIC). The novelty of Nano-MUSIC is that it can achieve super resolution image by using array signal processing technique and speckle illumination, by converting super resolution image to multiple source localization problem. Using Nano-MUSIC with focus stabilization, we demonstrate the multi-color 3D imaging with biological sample such as microtubule, mitochondria, F-actin to discover the sub-diffraction-scale details of cellular structures.