Transparent optoelectronic synapses are attracting great attention due to their great potentials in constructing "invisible" electronic products. In this work, CuI, a p-type semiconductor with good conductivity and transparency, is adopted as the electrode material. A transparent optoelectronic synapse is fabricated with a structure of CuI/copper-phthalocyanine (CuPc)/indium-tin oxide. The device shows a sensitive and linear response to the light stimulation with a wavelength of 660 nm. Some basic functions of biological synapses, such as pairedpulse facilitation, spike-rate-dependent plasticity, spike-numberdependent plasticity, and so forth, are successfully simulated by this transparent optoelectronic synapse. Furthermore, based on the high linear relationship between the device response and the number of light pulses, basic arithmetic operations of addition, subtraction, multiplication, and division within 20 are realized. The experimental results not only show the good performance of the device as an artificial synapse but also illustrate the great application potential of CuI in transparent and metallic electrode-free optoelectronics.