In this paper, we introduce a mixed- analog-to-digital converter (ADC) architecture for massive multiple-input multiple-output (MIMO) systems and study the system's performance mainly includes the achievable spectral efficiency and energy efficiency. In principle, the mixed-ADC architecture permits the one part of antennas at the base station (BS) are connected to speed and expensive full-resolution ADCs and the remaining part of the antennas are connected to the cheap low-resolution ADCs. By applying the general maximum-ratio combining detector, a tractable approximate expression for the achievable SE is obtained. Leveraging on the derived results, the effects of the number of BS antennas and the percent of the full-resolution ADCs on the achievable SE are investigated. Results show that the achievable SE increases with the percent of the full-resolution ADCs and the number of BS antennas. Based on a realistic power consumption model, we evaluate the energy efficiency for the considered mixed-ADC architecture. Moreover, under the certain achievable SE constraint, we maximize the energy efficiency by adjusting the number of low-resolution ADCs and the resolution bits of the corresponding ADC device. Numerical results showcase that the energy efficiency can be improved by enhancing the average transmitted power, and there exists an optimal number of resolution bits and the number of antennas to maximize the energy efficiency, which indicates that the application of mixed-ADC architecture has a great potential in future mobile communication system.