The single-degenerate (SD) model is one of the most popular progenitor models of type Ia supernovae (SNe Ia), in which the companion star can survive after an SN Ia explosion and show peculiar properties. Therefore, searching for the surviving companion in type la supernova remnants (SNRs) is a potential method to verify the SD model. In the SN 1604 remnant (Kepler's SNR), although Chandra X-ray observation suggests that the progenitor is most likely a WD+AGB system, the surviving companion has not been found. One possible reason is rapid rotation of the white dwarf (WD), causing explosion of the WD to be delayed for a spin-down timescale, and then the companion evolved into a WD before the supernova explosion, so the companion is too dim to be detected. We aim to verify this possible explanation by carrying out binary evolution calculations. In this paper, we use Eggleton's stellar evolution code to calculate the evolution of binaries consisting of a WD+red giant (RG). We assume that the rapidly rotating WD can continuously increase its mass when its mass exceeds the Chandrasekhar mass limit (M-ch = 1.378 M-circle dot) until the mass-transfer rate decreases to be lower than a critical value. Eventually, we obtain the masses of a WD in the range 1.378 M-circle dot to 2.707 M-circle dot. We also show that if the spin-down time is less than 10(6) yr, the companion star will be very bright and easily observed; but if the spin-down time is as long as similar to 10(7) yr, the luminosities of the surviving companion would be lower than the detection limit. Our simulation provides guidance in hunting for the surviving companion stars in SNRs, and the fact that no surviving companion has been found in Kepler's SNR may not be definite evidence disfavoring the SD origin of Kepler's SN.