Spiking neural network (SNN) is a brain-inspired model which has more spatio-temporal information processing capacity and computational energy efficiency. However, with the increasing depth of SNNs, the memory problem caused by the weights of SNNs has gradually attracted attention. Inspired by Artificial Neural Networks (ANNs) quantization technology, binarized SNN (BSNN) is introduced to solve the memory problem. Due to the lack of suitable learning algorithms, BSNN is usually obtained by ANN-to-SNN conversion, whose accuracy will be limited by the trained ANNs. In this paper, we propose an ultra-low latency adaptive local binary spiking neural network (ALBSNN) with accuracy loss estimators, which dynamically selects the network layers to be binarized to ensure the accuracy of the network by evaluating the error caused by the binarized weights during the network learning process. Experimental results show that this method can reduce storage space by more than 20 % without losing network accuracy. At the same time, in order to accelerate the training speed of the network, the global average pooling(GAP) layer is introduced to replace the fully connected layers by the combination of convolution and pooling, so that SNNs can use a small number of time steps to obtain better recognition accuracy. In the extreme case of using only one time step, we still can achieve 92.92 %, 91.63 % ,and 63.54 % testing accuracy on three different datasets, FashionMNIST, CIFAR-10, and CIFAR-100, respectively.