This paper considers testing for linear regression model when covariates are measured with additive error and some additional linear restrictions on the coefficients are available. We propose a test statistic based on the difference between the corrected residual sums of squares under the null and alterative hypotheses, and show that its limiting distribution is a weighted sum of independent chi-square distributions. We also develop an adjusted test statistic, which has an asymptotically standard chi-squared distribution. Finally, some simulations are given to examine the performance of our procedure and the results are satisfactory.