This paper investigates a variant of the work-stealing algorithm that we call the localized work-stealing algorithm. The intuition behind this variant is that because of locality, processors can benefit from working on their own work. Consequently, when a processor is free, it makes a steal attempt to get back its own work. We call this type of steal a steal-back. We show that the expected running time of the algorithm is $T_1/P+O(T_\infty P)$, and that under the "even distribution of free agents assumption", the expected running time of the algorithm is $T_1/P+O(T_\infty\lg P)$. In addition, we obtain another running-time bound based on ratios between the sizes of serial tasks in the computation. If $M$ denotes the maximum ratio between the largest and the smallest serial tasks of a processor after removing a total of $O(P)$ serial tasks across all processors from consideration, then the expected running time of the algorithm is $T_1/P+O(T_\infty M)$.