Inclusion Criteria:  Patients must be 18-75 years-of-age; Patients with Histologically or cytologically confirmed diagnosis of advanced or recurrent (Stage IIIB and IIIC not amenable for multimodality treatment) or metastatic (Stage IV) NSCLC that is ALK-positive where ALK status is determined by the NMPA-approved (for use in China) Ventana (D5F3) immunohistochemistry (IHC) test or FISH or PCR or NGS, Sufficient tumor tissue available to perform ALK status is required if not determined. Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) score of 0 to 2; Life expectancy of at least 12 weeks; Ability to swallow and retain oral medication;  Adequate organ system function, defined as follows:  Absolute neutrophil count (ANC) ≥1.5 x 109/L; Platelets ≥100 x 109/L; Hemoglobin ≥9 g/dL (≥90 g/L) Total bilirubin ≤1.5 times the upper limit of normal (ULN); Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤2.5 *ULN if no liver involvement or ≤5 * ULN with liver involvement. Creatinine < 1.5 *ULN. If >1.5 * ULN, patient may still be eligible if calculated creatinine clearance >50 mL/min (0.83mL/s) as calculated by the Cockcroft-Gault method. No prior systemic treatment for advanced or recurrent NSCLC (Stage IIIB and IIIC not amenable for multimodality treatment) or metastatic (Stage IV) NSCLC Tumor Requirements: At least 1 extracranial measurable target lesion per RECIST v. 1.1 that has not been previously irradiated. Serum pregnancy test (for females of childbearing potential) negative at screening. Ability to understand the nature of this trial and give written informed consent.  Exclusion Criteria:  Patients who meet any of the following criteria will be excluded from study entry:  Patients with a previous malignancy within the past 3 years are excluded (other than curatively treated basal cell carcinoma of the skin, early gastrointestinal (GI) cancer by endoscopic resection, in situ carcinoma of the cervix, or any cured cancer that is considered to have no impact in PFS and OS for the current NSCLC). Any GI disorder that may affect absorption of oral medications, such as mal-absorption syndrome or status post-major bowel resection ; Active and clinically significant bacterial, fungal, or viral infection including hepatitis B virus (HBV) or hepatitis C virus (HCV) (eg, in case of known HBsAg or HCV antibody positivity), known human immunodeficiency virus (HIV), or acquired immunodeficiency syndrome (AIDS)-related illness;  Clinically significant vascular (both arterial and venous) and non-vascular cardiac conditions, (active or within 3 months prior to enrollment), which may include, but are not limited to:  Arterial disease such as cerebral vascular accident/stroke (including Transient Ischemic Attack -TIA), myocardial infarction, unstable angina; Venous diseases such as cerebral venous thrombosis, symptomatic pulmonary embolism; Non-vascular cardiac disease such as congestive heart failure (New York Heart Association Classification Class ≥ II), second-degree or third-degree AV block (unless paced) or any AV block with PR >220 msec; or ongoing cardiac dysrhythmias of NCI CTCAE Grade ≥2, uncontrolled atrial fibrillation of any grade, bradycardia defined as <50 bpm (unless patient is otherwise healthy such as long-distance runners, etc.), machine-read Electrocardiogram (ECG) with QTc >470 msec, or congenital long QT syndrome; Patients with predisposing characteristics for acute pancreatitis according to investigator judgment (eg, uncontrolled hyperglycemia, current gallstone disease) in the last month prior to randomization; History of extensive, disseminated, bilateral or presence of Grade 3 or 4 interstitial fibrosis or interstitial lung disease including a history of pneumonitis, hypersensitivity pneumonitis, interstitial pneumonia, interstitial lung disease, obliterative bronchiolitis, and pulmonary fibrosis; Concurrent use of known strong CYP3A4 inhibitors and inducers (consult the sponsor if in doubt whether a food or a drug falls into any of the above categories) within 7 days prior to the first dose of XZP-3621 or crizotinib. Participation in other studies involving investigational drug(s) within 2 weeks prior to study entry and/or during study participation; Pregnant female patients; breastfeeding female patients; History of organ transplant; Co-administration of anti-cancer therapies other than those administered in this study; Baseline QTc>470ms ; History of hypersensitivity to any of the additives in the XZP-3621 or crizotinib drug formulation; Any psychological condition that potentially hampers compliance with the study protocol requirements or follow-up procedures; this condition should be discussed with the participant before study entry.