All-optical binary convolution with a photonic spiking vertical-cavity surface-emitting laser (VCSEL) neuron is proposed and demonstrated experimentally for the first time, to the best of our knowledge. Optical inputs, extracted from digital images and temporally encoded using rectangular pulses, are injected in the VCSEL neuron, which delivers the convolution result in the number of fast (<100ps long) spikes fired. Experimental and numerical results show that binary convolution is achieved successfully with a single spiking VCSEL neuron and that all-optical binary convolution can be used to calculate image gradient magnitudes to detect edge features and separate vertical and horizontal components in source images. We also show that this all-optical spiking binary convolution system is robust to noise and can operate with high-resolution images. Additionally, the proposed system offers important advantages such as ultrafast speed, high-energy efficiency, and simple hardware implementation, highlighting the potentials of spiking photonic VCSEL neurons for high-speed neuromorphic image processing systems and future photonic spiking convolutional neural networks.