Phase-shifting profilometry (PSP) is one of the most widely available methods in three-dimensional (3D) measurement. However, PSP is not suitable for dynamic measurements due to multiple projections. The color fringe projection profilometry(CFPP) can encode three grayscale fringe patterns in a single color pattern, preserving the robustness of PSP while enabling dynamic measurements. But for the CFPP measurement system, color coupling and imbalance phenomena are inevitable between the RGB channels, which increases the measurement error. This paper proposes a background intensity calibration (BIC) method to correct the color imbalance and reconstruct 3D shapes by a single-shot projected-captured. First, capture a color fringe image and extract the background intensity by searching the upper and lower envelopes to get three background-free fringe images; Secondly, solve the normalized coefficient to balance the three background-free images. As a result, a color fringe image can be split into three phase-shifting fringe images with the normalized modulation intensity and good sinusoidal aiming to perform phase demodulation by three-step PSP; Thirdly, the demodulation phase is unwrapped using a simple solving fringe orders algorithm based on a positive and negative binarization (PNB) method. Several experiments on dynamic scenes were performed, verifying that the measurement speed and accuracy of the proposed BIC method are not limited by the object moving, which can achieve fast, dense, and accurate 3D measurements.