The predominant geometry for a neutron imaging experiment is that of a pinhole camera. This is primarily due to the difficulty in focusing neutrons due to the weak refractive index, which is also strongly chromatic. Proof of concept experiments demonstrated that neutron image forming lenses based on reflective Wolter mirrors can produce quantitative, high spatial resolution neutron images while also increasing the time resolution compared to the conventional pinhole camera geometry. Motivated by these results, we report the design of a neutron microscope where two Wolter mirrors replace condensing and objective lenses, in direct analogy with typical visible light microscopes. Ray tracing results indicate that this system will yield 3 μm spatial resolution images with an acquisition time of order <1 s (104 faster than currently possible at this spatial resolution) with a field of view of about 5 mm in diameter.