<p>This paper focuses on the quaternion Givens QR decomposition, and analyses its rounding error. First of all, we give the rounding errors of parameters of the quaternion Givens rotation by some quaternion floating-point operation rules. Subsequently, for the quaternion Givens QR decomposition, we research its backward rounding error by dividing Givens rotations into some disjoint Givens rotation groups. In the end, in light of the aforementioned results, we analyse the backward rounding error of the quaternion least squares (QLS) problem with column full rank.</p>