Next generation sequencing reads from RNA-seq studies expose private genotypes of individuals during computation. Here, we introduce pQuant, an algorithm that employs homomorphic encryption to ensure privacy-preserving quantification of gene expression from RNA-seq data across public and cloud servers. pQuant performs computations on encrypted data, allowing researchers to handle sensitive information without exposing it. Our evaluations demonstrate that pQuant achieves accuracy comparable to state-of-the-art non-secure algorithms like STAR and kallisto. pQuant is highly scalable and its runtime and memory do not depend on the number of reads. It also supports parallel processing to enhance efficiency regardless of the number of genes analyzed.