The negatively charged nitrogen-vacancy (NV) center in diamonds is known as the spin defect and using its electron spin, magnetometry can be realized even at room temperature with extremely high sensitivity as well as a high dynamic range. However, a magnetically shielded enclosure is usually required to sense weak magnetic fields because environmental magnetic field noises can disturb high sensitivity measurements. Here, we fabricated a gradiometer with variable sensor length that works at room temperature using a pair of diamond samples containing negatively charged NV centers. Each diamond is attached to an optical fiber to enable free sensor placement. Without any magnetically shielding, our gradiometer realizes a magnetic noise spectrum comparable to that of a three-layer magnetically shielded enclosure, reducing the noises at the low-frequency range below 1 Hz as well as at the frequency of 50 Hz (power line frequency) and its harmonics. These results indicate the potential of highly sensitive magnetic sensing by the gradiometer using the NV center for applications in noisy environments such as outdoor and in vehicles.