The main errors of a ring-laser weak magnetic field sensor are analysed and the methods to eliminate these errors are discussed. The error introduced by temperature coeffient of verdet constant of magneto-optical materials is derived theoretically. This is the main source of error due to temperature coefficient of a ring-laser weak magnetic field sensor after low expansion cavity materials and frequency stabitization technique have been used. The error introduced by Zeeman effect is given. The Zeeman effect error results from ihe magnetio field sensitivity of the gain, medium, and it is mixed with the magnetio field sensitivity of the Faraday magnetio-optical material. Bj locating a gain tube in each longer arm of the rectangular cavity, the Zeeman effect can be avoided. The two gain tubes haye the same parameters (such as core length, diameter, total and partial presure, discharge current and diamension of catitod). The infiuenoe of Langmuir gas flow effect can be eidmination by beating positive and negative rotations and then adding the beats of right and ligt rotations.