Introduction Substance abuse remains one of the major challenges in young people, as it is one of the top five causes of disability-adjusted life years (DALY). The present study aims to find the prevalence and determinants of substance use among young people attending an urban primary health center in Delhi. Methodology Systematic random sampling was used to enroll the calculated sample size of 190. Substance use was assessed using ASSIST (an Alcohol Smoking Substance Involvement Screening Tool) and brief intervention was given based on the standard guidelines of ASSIST. The total score among the substance users is calculated and divided into Grades 1, 2 or 3. Log binomial regression was performed to quantify the association between substance use and covariates such as age, sex, education, occupation, family history of substance use, socio-economic status and family type. The association was expressed in odds ratio (OR) with 95 percent confidence interval (CI). Result The mean age of study participants was 18.6 ± 4.1, ranges from 10 to 24 years. Out of 48 substance users, 43.7% were consuming only tobacco, 22.9% were consuming only alcohol and 33.3% were polysubstance users. The history of substance use among family members of participants was found to be 46.3%. Median substance involvement score of tobacco, alcohol and cannabis users was 19 (IQR: 14.5–22), 19 (IQR: 13.5–25) and 22.5 (IQR: 22–23), respectively. Among tobacco users, 2.7% were Grade 1 and 7.2% were Grade 2. Four (16%), 20 (80%) and one (4%) of alcohol users were Grades 1, 2 and 3, respectively. Among the cannabis users, four (100%) were in the Grade 2 category. The median age of initiation of substance use among users was 16 (range 13–21) years. The analysis shows substance use was almost 25 times (adjusted OR = 25.84, 95% CI 5.65–118.09) more common among males and it increase by 2.5 times with a decrease in socio-economic status (adjusted OR = 2.52, 95% CI 1.27–5.02) and the result is significant. The substance use was almost 7 times higher when there is a family history of substance usage (adjusted OR = 7.40, 95% CI 2.15–25.4). Residential and marital status were not significantly associated with substance use. Conclusion Male sex, lower socio-economic status, participants currently not going to school/college, family history of substance use were found to be significant predictors of substance use among the study participants.