Two-dimensional (2D) solar coronal magnetogram is difficult to be measured directly until now. From the previous knowledge, a general relation has been noticed that the brighter green-line brightness for corona, the higher coronal magnetic field intensity may correspond to. To try to further reveal the relationship between coronal green line brightness and magnetic field intensity, we use the 2D coronal images observed by Yunnan Observatories Green-line Imaging System (YOGIS) of the 10 cm Lijiang coronagraph and the coronal magnetic field maps calculated from the current-free extrapolations with the photospheric magnetograms taken by Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) spacecraft. In our analysis, we identified the coronal loop structures and construct two-dimensional maps of the corresponding magnetic field intensity in the plane of the sky (POS) above the limb. We derive the correlation coefficients between the coronal brightness and the magnetic field intensity for different heights of coronal layers. We further use a linear combination of a Gaussian and a quadratic profile to fit the correlation coefficients distribution, finding a largest correlation coefficient of 0.82 near 1.1 R (circle dot) (solar radii) where is almost the top of the closed loop system. For the small closed loop system identified, the correlation coefficient distributions crossing and covering the loop are calculated. We also investigate the correlation with extended heliocentric latitude zones and long period of one whole Carrington Rotation, finding again that the maximum correlation coefficient occurs at the same height. It is the first time for us to find that the correlation coefficients are high (all are larger than 0.8) at the loop-tops and showing poor correlation coefficients with some fluctuations near the feet of the coronal loops. Our findings indicate that, for the heating of the low-latitude closed loops, both DC (dissipation of currents) and AC (dissipation of Alfven and magnetosonic waves) mechanisms should act simultaneously on the whole closed loop system while the DC mechanisms dominate in the loop-top regions. Therefore, in the distributions of the correlation coefficients with different heights of coronal layers, for both large- and small-scale latitude ranges, the coefficients can reach their maximum values at the same coronal height of 1.1 R (circle dot), which may indicate the particular importance of the height of closed loops for studying the coupling of the local emission mechanism and the coronal magnetic fields, which maybe helpful for studying the origin of the low-speed solar wind.