We considered the least squares estimation and the ridge estimation of regression coefficient in the heterogeneous restricted linear regression model. When the design matrix X is all ill-conditioned matrix, the least squares estimation is no longer a good estimation, The paper proposes a new restricted ridge estimation, obtains from the restricted condition, with the aid of condition extreme value, we study the minimization of (Y-Xβ)′(Y-Xβ),and cause the question to transform as optimized question under two restricted conditions.