This paper proposes a method for motion estimation of consecutive cameras using 3-D straight lines. The motion estimation algorithm uses two non-parallel 3-D line correspondences to quickly establish an initial guess for the relative pose of adjacent frames, which requires less correspondences than that of current approaches requiring three correspondences when using 3-D points or 3-D planes. The estimated motion is further refined by a nonlinear optimization technique with inlier correspondences for higher accuracy. Since there is no dominant line representation in 3-D space, we simulate two line representations, which can be thought as mainly adopted methods in the field, and verify one as the best choice from the simulation results. We also propose a simple but effective 3-D line fitting algorithm considering the fact that the variance arises in the projective directions thus can be reduced to 2-D fitting problem. We provide experimental results of the proposed motion estimation system comparing with state-of-the-art algorithms using an open benchmark dataset.