Fuzzing has shown great success in evaluating the robustness of intelligent natural language processing (NLP) software. As large language model (LLM)-based NLP software is widely deployed in critical industries, existing methods still face two main challenges: 1 testing methods are insufficiently coupled with the behavioral patterns of LLM-based NLP software; 2 fuzzing capability for the testing scenario of natural language generation (NLG) generally degrades. To address these issues, we propose BASFuzz, an efficient Fuzz testing method tailored for LLM-based NLP software. BASFuzz targets complete test inputs composed of prompts and examples, and uses a text consistency metric to guide mutations of the fuzzing loop, aligning with the behavioral patterns of LLM-based NLP software. A Beam-Annealing Search algorithm, which integrates beam search and simulated annealing, is employed to design an efficient fuzzing loop. In addition, information entropy-based adaptive adjustment and an elitism strategy further enhance fuzzing capability. We evaluate BASFuzz on six datasets in representative scenarios of NLG and natural language understanding (NLU). Experimental results demonstrate that BASFuzz achieves a testing effectiveness of 90.335% while reducing the average time overhead by 2,163.852 seconds compared to the current best baseline, enabling more effective robustness evaluation prior to software deployment.