A capacitive probe [Mingsheng, Tan, et al. Rev. Sci. Instrum 88, 023502 (2017)] is one of a few diagnostics that is directly sensitive to the plasma potential. Using this diagnostic technique, a Multi-channel Linear Capacitive Probe (MLCP) is developed for turbulence measurements. The MLCP has 10 spatial channels and provides 9 points of radial electric field measurements simultaneously with a spatial step of 7 mm. A new readout circuit and a correction technique for low frequency attenuation are also developed to achieve the required spatial and time resolution. A performance test of the MLCP using a reversed field pinch plasma confirms that the MLCP resolves sub-centimeter structures of the equilibrium radial electric field profile and fluctuations up to 680 kHz.