Tobacco smoking continues to be a leading cause of disease and mortality. Recent research has confirmed the important role of nicotinic acetylcholine receptor (nAChR) gene cluster on chromosome 15q 24-25 in nicotine dependence and smoking. In this study we tested the association of smoking initiation, age at onset of daily smoking, and heaviness of smoking with five single nucleotide polymorphisms (SNPs) within the CHRNA5-CHRNA3-CHRNB4 cluster. The group of 389 adult subjects of European ancestry from the north of Poland, including 212 ever (140 current and 72 former) and 177 never smokers with mean age 49.26, was genotyped for rs16969868, rs1051730, rs588765, rs6495308, and rs578776 polymorphisms. Distributions of genotypes for rs16969868 and rs1051730 were identical so they were analyzed together. Further analysis revealed the association between rs16969868-1051730 (OR = 2.66; 95% CI: 1.30–5.42) and number of cigarettes smoked per day (CPD) with heaviness of nicotine addiction measured by the Fagerström Test for Nicotine Dependence (FTND) (OR = 2.60; 95% CI: 1.24–5.43). No association between these polymorphisms and other phenotypes was found. Similarly, the association between rs588765, rs6495308, rs578776, and analyzed phenotypes was not confirmed. This study provides strong evidence for the role of the CHRNA5-CHRNA3-CHRNB4 cluster in heaviness of nicotine addiction.