Background: In recent years, due to the difficulty and inefficiency of experimental methods, numerous computational methods have been introduced for inferring structure of Gene Regulatory Networks (GRNs). Bayesian network is one of the popular methods in this field, however, still has many drawbacks and there is still a great space to be improved. For example, the Path Consistency (PC)-based algorithms as Bayesian network methods are still sensitive to the ordering of nodes i.e. different node orders results in different network structures. The second is that the networks inferred by these methods are highly dependent on the threshold used for independence testing. Also, it is still a challenge to select the set of conditional genes in an optimal way, which affects the performance and computation complexity of the PC-based algorithm. Results: We introduce a novel algorithm, namely Order Independent PC-based algorithm using Quantile value (OIPCQ), which improves the accuracy of the learning process of GRNs and solves the order dependency issue. The quantile-based thresholds are considered for different order of CMI test. For conditional gene selection, we consider the paths between genes with length equal or greater than 2 while others well-known PC-based methods only considers the paths of length 2. We applied OIPCQ on the various networks of the DREAM3 and DREAM4 in silico challenges. As a real-world case study, we used OIPCQ to reconstruct SOS DNA network obtained from Escherichia coli and GRN for acute myeloid leukemia based on the RNA sequencing data from The Cancer Genome Atlas. The results show that OIPCQ produces the same network structure for all the permutations of the genes and improves the resulted GRN through accurately quantifying the causal regulation strength in comparison with others well-known PC-based methods. Conclusions: According to the GRN constructed by OIPCQ, for acute myeloid leukemia, two regulators BCLAF1 and NRSF reported by Zhang et al are significantly important. However, the highest degree nodes in this GRN are ZBTB7A and PU1 which play a significant role in cancer, and especially in leukemia. OIPCQ is freely accessible at https://github.com/haammim/OIPCQ-and-OIPCQ2.