In this paper an error analysis of 3-dimensional GNSS attitude determination system is given. The attitude error covariance matrix is derived and analyzed. It implies that attitude errors are affected by the baseline length and configuration, the satellites numbers and geometry, receiver measurement noises and the nominal attitude of the vehicle. By defining Euler Angle Dilution Of Precision (EADOP) which is analogous to GDOP, roll, pitch and yaw errors can be efficiently analyzed. However the expression of the attitude error is too complex to get some intuitions. Therefore with a commonly adopted assumption, new expressions for attitude error are derived. The formulas are easy to compute and represent the attitude error as a function of the nominal attitude of a vehicle, the baseline configuration and the receiver noise. Using the formula, the accuracy of the attitude can be analytically predicted without the computer simulations. Applications to some widely used configurations reveal the effectiveness of the proposed method.