We report on the determination of fluorescence resonance energy transfer (FRET) efficiency, which is dependent on the donor-to-acceptor (D-A) ratio, by using a new type of microchannel device called a "lipid-flow chip". The chip comprises two supported lipid bilayers (SLBs) that self-spread from either side of 10 mu m wide straight lines and carry molecules embedded in them. We first show that the diffusion process that occurs when the two SLBs collide with each other in the channel and form a unified SLB can be expressed by a one-dimensional diffusion equation. Next we describe a method for determining the FRET efficiency between NBD (donor) and Texas Red (acceptor) from observations using the lipid-flow chip by employing a one-dimensional diffusion model. The advantages of our method are that all the D-A ratios are achieved in one chip, and a large number of data are recorded in one chip. The FRET efficiency varies depending on the D-A ratio under conditions whereby the concentration of the sum of the donors and acceptors is constant. The Forster radius is also estimated from our,results using a known model describing two-dimensional FRET systems, which yields a radius consistent with the previously reported value for NBD and Texas Red.