We investigated numerically localization properties of electron eigenstates in a chain with long-range correlated diagonal disorder. A tight-binding one-dimensional model with on- site energies exhibiting long-range correlated disorder (LCD) was used with various disorder strength W. LCD was defined so that it gave a power-law spectral density of the form S(k) ak(-p), where p determines the roughness of the potential landscape. Numerical results on the correlation length. of eigenstates shows the existence of the localization-delocalization transition at p = 2. It is found that the critical values for disorder strength W-c and also the critical exponent. for localization length change with the values of p.