The resistive switching characteristics of indium tin oxide (ITO)/Zn1-xCoxO/ITO transparent resistive memory devices were investigated. An appropriate amount of cobalt dopant in ZnO resistive layer demonstrated sufficient memory window and switching stability. In contrast, pure ZnO devices demonstrated a poor memory window, and using an excessive dopant concentration led to switching instability. To achieve suitable memory performance, relying only on controlling defect concentrations is insufficient; the grain growth orientation of the resistive layer must also be considered. Stable endurance with an ON/OFF ratio of more than one order of magnitude during 5000 cycles confirmed that the Co-doped ZnO device is a suitable candidate for resistive random access memory application. Additionally, fully transparent devices with a high transmittance of up to 90% at wavelength of 550 nm have been fabricated.