Alzheimer's disease (AD) is the prevalent form of dementia and shares many aspects with the aging pattern of the abnormal brain. Machine learning models like support vector regression (SVR) based models have been successfully employed in the estimation of brain age. However, SVR is computationally inefficient than twin support vector machine based models. Hence, different twin support vector machine based models like twin SVR (TSVR), ε-TSVR, and Lagrangian TSVR (LTSVR) models have been used for the regression problems. ε-TSVR and LTSVR models seek a pair of ε-insensitive proximal planes for generation of end regressor. However, SVR and TSVR based models have several drawbacks- i) SVR model is computationally inefficient compared to the TSVR based models. ii) Twin SVM based models involve the computation of matrix inverse which is intractable in real world scenario's. iii) Both TSVR and LTSVR models are based on empirical risk minimization principle and hence may be prone to overfitting. iv) TSVR and LTSVR assume that the matrices appearing in their formulation are positive definite which may not be satisfied in real world scenario's. To overcome these issues, we formulate improved least squares twin support vector regression (ILSTSVR). The proposed ILSTSVR modifies the TSVR by replacing the inequality constraints with the equality constraints and minimizes the slack variables using squares of L2 norm instead of L1. Also, we introduce a different Lagrangian function to avoid the computation of matrix inverses. We evaluated the proposed ILSTSVR model on the subjects including cognitively healthy, mild cognitive impairment and Alzheimer's disease for brain-age estimation. Experimental evaluation and statistical tests demonstrate the efficiency of the proposed ILSTSVR model for brain-age prediction.