The main factors that enable capture of complex and transient signals in real-time are improved sampling rates and processing speeds. The time-interleaved architecture is an effective method that allows systems to break through the speed bottleneck of single analog-to-digital converters (ADCs) and go beyond the state-of-the-art process technology limit. However, the performance of the acquisition system may be reduced because of the offset, gain, and time mismatch errors that occur in time-interleaved ADC systems. To correct these errors, this paper first proposes a self-adaptive correction algorithm and then introduces real-time solutions for this algorithm. Finally, the proposed calibration method is implemented in a digital phosphor oscilloscope. Simulations and experimental testing indicate that this system shows good real-time performance and provides a high dynamic performance with an effective number of bits of 7.3 bits and a signal-to-noise ratio of 45.5574 dB.