Mealiness in apple fruit can occur during storage or because of harvesting in an inappropriate time; it degrades the quality of the fruit and has a considerable role in the fruit industry. In this paper, a novel non-destructive approach for detection of mealiness in Red Delicious apple using acoustic and deep learning techniques was proposed. A confined compression test was performed to assign labels of mealy and non-mealy to the apple samples. The criteria for the assignment were hardness and juiciness of the samples. For the acoustic measurements, a plastic ball pendulum was used as the impact device, and a microphone was installed near the sample to record the impact response. The recorded acoustic signals were converted to images. Two famous pre-trained convolutional neural networks, AlexNet and VGGNet were fine-tuned and employed as classifiers. According to the result obtained, the accuracy of AlexNet and VGGNet for classifying the apples to the two categories of mealy and non-mealy apples was 91.11% and 86.94%, respectively. In addition, the training and classification speed of AlexNet was higher. The results indicated that the suggested method provides an effective and promising tool for assessment of mealiness in apple fruit non-destructively and inexpensively.