Arterial spin labeling (ASL) is an MRI perfusion imaging method from which quantitative cerebral blood flow (CBF) can be calculated. We present a multi-TI ASL method (multi-TI integrated ASL) in which variable post-labeling delays and variable TRs are used to improve the estimation of arterial transit time (ATT) and CBF while shortening the scan time by 41% compared to the conventional methods. Variable bolus widths allow for T1 and M0 estimation from raw ASL data. Multi-TI integrated pseudo-continuous ASL images were collected at 7 TI times ranging 100-4300 ms. Voxel-wise T1 and M0 maps were estimated, then CBF and ATT maps were created using the estimated T1 tissue map. All maps were consistent with physiological values reported in the literature. Based on simulations and in vivo comparisons, this method demonstrates higher CBF and ATT estimation efficiency than other ATT acquisition methods and better fit to the perfusion model. It produces CBF maps with reduced sensitivity to errors from ATT and tissue T1 variations. The estimated M0, T1, and ATT maps also have potential clinical utility. The method requires a single scan acquired within a clinically acceptable scan time (under 6 minutes) and with low sensitivity to motion.