This paper presents an improvement of the capacitive emulation (CE) method to reduce the line current distortion caused by grid-tied LCL-filtered converters. In these cases, the grid voltage is applied to the LCL's capacitor, which generates a distorted capacitor current that pollutes the line. The CE method consists in controlling the converter currents instead of the grid currents, while the converter generates a copy of the distorted capacitor current, so that both the copy and the distorted currents cancel each other in the grid. Therefore, we can say that the converter emulates a negative capacitance connected to the grid, while at the same time delivers its active and reactive powers at the fundamental frequency. The CE method is achieved by adding an estimation of the distorted capacitor current to the converter current reference. However, an effective capacitive emulation requires a current control capable of accurately tracking all harmonics added to the current reference. In this sense, this paper proposes the use of a new integral predictive current control (IPCC), a dead-beat type of control that ensures a constant closed-loop group delay in a wide bandwidth. Unlike a PI control where the closed-loop delay varies with the frequency of the tracked harmonic, the constant control delay of the IPCC can be effectively compensated with a buffer-based advanced current reference. The effectiveness of the proposed CE method with IPCC control to reduce the total harmonic distortion (THD) of the line currents has been proved experimentally on a 10 kVA transformerless grid-connected three-phase inverter.