Crizotinib, a small molecular tyrosine kinase inhibitor, manifests dramatic responses in patients with non-small cell lung cancer with echinoderm microtubule associated protein like 4-anaplastic lymphoma kinase (EML4-ALK) rearrangements. ALK gene point mutation is the primary mechanism of acquired crizotinib resistance; however, the intrinsic mechanism is not fully understood. Here, we report a patient with a low mutant allele fraction (MAF) of EML4-ALK rearrangement, who experienced primary resistance to crizotinib treatment. The patient was a 66-year-old Chinese man, who had a history of metastatic lung cancer and was treated with first- and third-generation epidermal growth factor receptor tyrosine kinase inhibitors (EGFR TKIs). After 14 months of osimertinib treatment, his disease progressed, and next-generation sequencing was performed from a liquid biopsy of the patient’s blood. An EML4-ALK rearrangement was found and crizotinib was administered. The patient’s lung lesions continued to progress after one month of crizotinib treatment, and pemetrexed-bevacizumab was initiated. After two cycles of chemotherapy, the metastatic cancers shrunk, and the patient maintained stable disease at his last follow-up. EML4-ALK rearrangements can happen in patients with EGFR-positive NSCLC, after acquired resistance to EGFR TKI treatment. The EGFR T790M and C797G mutations occur in cis is a critical mechanism of resistance to osimertinib therapy. The MAF of EML4-ALK rearrangements in cancer cells might be a predictive factor for crizotinib treatment.