We propose a specially designed plasmonic lens structure to succeed in realizing sub-diffraction phase-contrast imaging of transparent nano-objects. The nano-objects are embedded inside the insulator layer of the metal-insulator-metal (MIM) plasmonic structure and have a small refractive index difference with respect to the transparent insulator layer. The excited surface plasmons in the MIM structure help to greatly enhance scattered light from the nano-objects and effectively suppress the transmitted illumination light. A spatial resolution of about 64 nm and a minimum distinguishable refractive index difference down to 0.05 are numerically demonstrated. For sub-diffraction phase-contrast imaging of irregular three-dimensional (3D) nanowires and nanocylinders, the optimized MIM structure shows much better performance in comparison with that of a superlens.