As nanotechnology has developed, precision measurement on a nanometer order (nanometrology) has become important. In order to meet this demand, we have developed and investigated an AFM system with a high-resolution three-axis laser interferometer (nanometrological AFM). We have performed precision measurements of 1-dimensional (1D) gratings as a nano-dimensional scale and uncertainty estimation in pitch measurements. The calibrated dimensions of AFM images are traceable to the international unit of length through a laser wavelength. The resolution of the interferometer was approximately 0.04 nm. For a pitch measurement of a 1D grating with a 240 nm pitch in nominal value, we obtained a pitch value of 239.98 nm and estimated an expanded uncertainty of 0.280 nm.