Nonvolatile processors (NVPs) have strong vitality in battery-less energy-harvesting sensor nodes (EHSNs) due to their characteristics of zero standby power, resilience to power failures, and fast read/write operations. However, I/O and sensing operations cannot store their system states after power OFF; hence, they are sensitive to power failures and high power switching overhead is induced during power oscillation, which significantly degrades the system performance. In this paper, we propose a novel performance-aware task scheduling technique considering power switching overhead for energy-harvesting NVPs. We first present the analysis of the power switching overhead on EHSNs. Then, the scheduling problem is formulated by mixed-integer linear programming (MILP). Furthermore, offline and online performance-aware heuristic scheduling algorithms with the task splitting (TS) strategy are proposed to solve the scheduling problem efficiently. Experimental results show that comparing with the state-of-the-art energy-harvesting oblivious scheduling strategy, the proposed MILP scheduling approach can improve the performance by 16% on average, and the proposed scheduling algorithm with the TS strategy can reduce the average execution time by 24.8% and 22.5%.