This study proposes a self-powered food monitoring system that benefits from far-field RF Energy harvesting and deep learning techniques. Recent smart IoT systems for food quality management mainly focused on the appearance of Total Volatile Organic Compounds (TVOCs) during food preservation, which has the limitations of large power consumption, complex configuration, and low accuracy. Different from these methods, we aim to measure the gradual increase in air pressure inside food packages caused by gas emissions during food quality deterioration. With this new approach, the designed sensor circuit's energy consumption is reduced significantly than in conventional systems. The sensor module's operation power is supplied by an RF energy harvester capable of converting electromagnetic waves in space into electrical energy. We adopted a Yagi three elements as a receiver antenna in the RF energy scavenging module to enhance the harvested power and transmission distance. The designed antenna has a high gain of 6.54dBi in the direction of maximum radiation and voltage standing wave ratio (VSWR) better than 1.3 in approximately 60 MHz band (890-950 MHz). To demonstrate the feasibility of the proposed system, a set of experiments were conducted with different sorts of food such as pork, chicken, and fish. Raw data of food storage temperature, air pressure, and storage time obtained from the battery-less sensor module were analyzed and utilized to assess food quality changes. Several classification models, including LSTM, 1D-CNN, MLP, and SVM were developed and trained on the pork, chicken, and fish datasets to predict different food quality states. Experimental results show that the LSTM classifier, which can extract temporal characteristics from the dataset, achieves the best accuracy of above 99% on all three datasets. The food classification performance is investigated based on training accuracy and confusion matrix.