In the article, we introduce both the theoretical analysis and proof-of-principle experimental results of a novel transmission-line microwave interferometer (TLMI) for measurements of plasma density. The principle of this technique is the same as conventional microwave interferometers except that the sensing microwave propagates along a transmission-line structure. For this study, the transmission-line is a circular coaxial dielectric waveguide operated at 2.4 GHz. A microwave module of the TLMI system, consisting of a microwave source and a phase detector, has also been developed for detecting the phase of the microwave propagating through the transmission-line. The measurement of the TLMI system shows a real-time and complete response to the plasma source. The result of plasma density measured by the interferometer is well consistent with that from a Langmuir probe.