Metallicity gradients refer to the sloped radial profiles of the metallicities of gas and stars and are commonly seen in disk galaxies. A well-defined metallicity gradient of the Galactic disk is observed particularly well with classical Cepheids, which are good stellar tracers thanks to their period-luminosity relation, allowing precise distance estimation and other advantages. However, the measurement of the inner-disk gradient has been impeded by the incompleteness of previous samples of Cepheids and the limitations of optical spectroscopy in observing highly reddened objects. Here we report the metallicities of 16 Cepheids measured with high-resolution spectra in the near-infrared YJ bands. These Cepheids are located at 3-5.6 kpc in Galactocentric distance, R-GC, and reveal the metallicity gradient in this range for the first time. Their metallicities are mostly between 0.1 and 0.3 dex in [Fe/H] and more or less follow the extrapolation of the metallicity gradient found in the outer part, R-GC > 6.5 kpc. The gradient in the inner disk may be shallower or even flat, but the small sample does not allow the determination of the slope precisely. More extensive spectroscopic observations would also be necessary for studying minor populations, if any, with higher or lower metallicities that were reported in previous literature. In addition, the 3D velocities of our inner-disk Cepheids show a kinematic pattern that indicates noncircular orbits caused by the Galactic bar, which is consistent with the patterns reported in recent studies on high-mass star-forming regions and red giant branch stars.