Computer technology's rapid advancement has significantly enhanced global agricultural modernization, notably improving agricultural production efficiency. Given the vulnerability of strawberries during the harvesting process, the automatic harvesting technology for strawberries necessitates a highly accurate recognition algorithm. In this paper, we introduce a model, Strawberry R-CNN, designed for intelligent recognition and counting of strawberries in natural environments. The Strawberry R-CNN model enhances strawberry recognition accuracy by refining the Faster R-CNN through several key modifications. Firstly, we replaced the VGG16 in the original Faster R-CNN with an improved multi-cascade network structure for feature extraction. This change allows for the capture of rich location data and detailed information typically absent in higher-level features. Secondly, the RoiPooling operation was replaced with RoiAlign to eliminate the error associated with the rounding method in two quantization stages. Lastly, we utilized a bilinear interpolation method for computation, preserving the floating-point number, and reducing model error. For strawberry counting, we proposed an efficient and practical evaluation method by creating an error set for strawberry counting. Experimental results demonstrated that the Strawberry R-CNN model achieved an average precision (AP) of 0.9019 for ripe strawberries and 0.8447 for immature ones, with a mean average precision (mAP) of 0.8733. The counting accuracy for ripe and immature strawberries was 99.1% and 73.7% respectively. The method presented in this work exhibits strong detection and counting capabilities, suitable for automatic monitoring, harvesting, and yield estimation of strawberries.