This paper presents a concept of a multiple channel picoammeter suitable for operation at a high voltage. To ensure floating operation, 1kHz readout rate and low battery usage, the picoammeter employs an optical fibre for data transmission. The analogue conditioning section consists of a transimpedance amplifier that is connected to a 16 bit ΣΔ ADC which is integrated into the microcontroller. Simultaneous reception of data sent from multiple picoammeter units is achieved using an FPGA device and a USB interface to the host PC. A prototype with a ±125nA range was constructed. The paper includes a calibration procedure of the prototype and an example of a current leakage test conducted on a 10×10cm2 GEM foil. The resolution achieved by the prototype in a 15min test at 0.5nA bias was 6.5pA FWHM.