We propose a new mixed-analog-to-digital convertor (mixed-ADC) architecture for cloud-RAN (C-RAN) systems. The RRH is equipped with a mixed-ADC pool that includes multiple ADC units with various resolutions. In this pool, the RRH selects the appropriate ADCs and connects the selected ADCs to each antenna to quantize the received signals, thereby each antenna can have a different resolution ADC. The quantized signals are sent to a centralized baseband unit (BBU) via a capacity limited fronthaul pipe. To maximize the spectral efficiency of the considered system in a single-user uplink phase, we formulate an optimization problem for ADC selection by exploiting an approximation of the generalized mutual information (GMI). Subsequently we propose a solution. The simulations show the improvement in the GMI by using the proposed ADC selection. Our major findings are: i) In a C-RAN with limited fronthaul capacity, the proposed mixed-ADC makes more efficient use of the fronthaul capacity. ii) In selecting ADCs, assigning a high resolution ADC to a strong channel is beneficial.