We present a portable multi-contrast microscope capable of producing bright-field, dark-field, and differential phase contrast images of thin biological specimens on a smartphone platform. The microscopy method is based on an imaging scheme termed "color-coded light-emitting-diode (LED) microscopy (cLEDscope)," in which a specimen is illuminated with a color-coded LED array and light transmitted through the specimen is recorded by a color image sensor. Decomposition of the image into red, green, and blue colors and subsequent computation enable multi-contrast imaging in a single shot. In order to transform a smartphone into a multi-contrast imaging device, we developed an add-on module composed of a patterned color micro-LED array, specimen stage, and miniature objective. Simple installation of this module onto a smartphone enables multi-contrast imaging of transparent specimens. In addition, an Android-based app was implemented to acquire an image, perform the associated computation, and display the multi-contrast images in real time. Herein, the details of our smartphone module and experimental demonstrations with various biological specimens are presented.