This is a study which consists of phase 1a study (dose escalation stage) and phase 1b study (expansion stage). Phase 1a study will adopt the classical 3+3 dose escalation design, exploring safety and tolerance of 4 dose cohorts (1mg/kg, 3mg/kg, 200mg and 10mg/kg) and determining the recommended dose for phase 1b study. Phase 1b will expand in 4 participant populations to further evaluate the safety and clinical activity of IBI308 monotherapy or in combination with chemotherapy: Cohort A (monotherapy in participants with advance melanoma), Cohort B (monotherapy in participants with advanced malignancies of the digestive system after failure of at least 1 line of standard therapy), Cohort C (monotherapy in participants with advanced non small cell lung cancer after failure or intolerance of 1st line therapy) and Cohort D (in combination with cisplatin and pemetrexed in treatment naive participants with inoperable locally advanced or advanced non-squamous non small cell lung cancer). Phase 1a and 1b consist of Screening Period (28 days before enrollment), Treatment Period and Follow up Period (every 3 months until death or the end of study). In phase 1a, dose limiting toxicity will be recorded for up to 28 days after the 1st dose of IBI308. Efficacy will primarily be evaluated by RECIST v1.1. Participants' safety will be monitored throughout the study. Further exploration of pharmacokinetic/pharmacodynamics and immunogenicity information will be assessed throughout the trial.