We report an application of nanoarea electron diffraction for structure determination of double-wall carbon nanotubes (DWNT) grown by catalytic chemical vapor deposition. The structures of 30 tubes were determined from experimental diffraction patterns. Among these tubes, the inner and outer wall structure of 18 tubes was precisely determined by comparison with kinematic electron diffraction simulations. For the structure of the DWNTs, our experiment revealed a mixture of semiconducting-metallic (S-M), S-S and M-M tubes. The spacing between the two walls ranges from 0.335 nm to 0.384 nm. Most DWNTs are incommensurate and chiral.