A chaotic signal in an observation area of network nodes is sent to a fusion center for reconstruction. As the communication bandwidth is limited, the signal must be quantified before sending to the fusion center, which will add quantization noise to the observed signal, which makes the signal reconstruction more difficult. A chaotic signal reconstruction algorithm is proposed in this paper based on square-root cubature Kalman filter. Firstly the probability density function of the observed signal is estimated, and then the optimal quantizer is used to quantify the observed signal. Under the limited budget of quantization bits, the best performance can be achieved. Compared with the unscented Kalman filter counterpart, our algorithm has fewer cubature points and has the merit of small computation load; meanwhile, it uses the square root of error variance for iteration, this will be more stable and accurate when iterating for parameter estimation. Simulation results show that the algorithm can reconstruct the observed signal quickly and effectively, with consuming less computation time and being more accurate than the one based on unscented Kalman filter.