Sunflower is one of the oilseed crops which is popularly and widely cultivated globally and contributes significantly to human health. Leaf diseases of sunflower seriously affect the growth and yield of sunflower, which directly leads to the loss of agricultural economy. However, existing machine learning algorithms and deep learning techniques are mainly based on large models with attention mechanisms, which lack considerations in computational performance, especially model size. Therefore, this study proposes a lightweight model called TeenyNet to break through the dilemma. First, the designed global multi-frequency feature extraction module decomposes the image to extract multi-frequency multi-scale features. Then, a parameter-free maximum pooling layer further extracts edge and texture features and simplifies the network complexity through downsampling, after which the proposed lightweight dual fusion attention and multi-branching structure fuses all the feature vectors to enhance multidimensional feature learning and accelerate the model convergence. Finally, the fully connected linear layer solves the multi-classification problem of sunflower disease under natural illumination background conditions. The experimental results show that TeenyNet obtains the highest accuracy of 98.94% for sunflower disease recognition with a minimum size of 143 KB and has better recognition performance in comparison experiments. TeenyNet can be effectively used for the detection of sunflower leaf diseases to achieve disease prevention and control.