A new method for measuring the global magnetic field structure of the Galactic plane is presented. We have determined the near-infrared polarization of field stars around 52 Cepheids found in recent surveys toward the Galactic plane. The Cepheids are located at the galactic longitudes $-10^{circ}leq , l, leq +10.5^{circ}$ and latitudes $-0.22^{circ}leq , l, leq +0.45^{circ}$, and their distances are mainly in the range of 10 to 15 kpc from the Sun. Simple classification of the sightlines is made with the polarization behavior vs. $H-K_{mathrm S}$ color of field stars, and typical examples of three types are presented. Then, division of the field stars in each line of sight into (a) foreground, (b) bulge, and (c) background is made with the $Gaia$ DR2 catalog, the peak of the $H-K_{mathrm S}$ color histogram, and $H-K_{mathrm S}$ colors consistent with the distance of the Cepheid in the center, respectively. Differential analysis between them enables us to examine the magnetic field structure more definitely than just relying on the $H-K_{mathrm S}$ color difference. In one line of sight, the magnetic field is nearly parallel to the Galactic plane and well aligned all the way from the Sun to the Cepheid position on the other side of the Galactic center. Contrary to our preconceived ideas, however, sightlines having such well-aligned magnetic fields in the Galactic plane are rather small in number. At least 36 Cepheid fields indicate random magnetic field components are significant. Two Cepheid fields indicate that the magnetic field orientation changes more than 45 in the line of sight. The polarization increase per color change $P$/ ($H-K_{mathrm S}$) varies from region to region, reflecting the change in the ratio of the magnetic field strength and the turbulence strength.
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