People from low socioeconomic positions (SEP) are at a higher risk of smoking, face greater barriers to smoking cessation, and have lower access to health information. To improve tobacco-related health outcomes, policies requiring altering labeling on cigarette packs could be implemented. However, public support is needed to influence the policymaking process. We assessed factors associated with supporting tobacco-control communication policies. We analyzed data from Project CLEAR, a study conducted in Massachusetts. The analytic sample included participants who answered questions on their support for three policies: 1) graphic health warnings (GHWs), 2) Quitline number, and 3) smoking cessation information on cigarette packs (n = 357). Binomial logistic regression modeling was conducted by policy. Independent variables included demographic characteristics and smoking status. We found that younger vs. older individuals (aOR = 0.41, 95 %CI:0.23–0.72), males vs. females (aOR = 0.58, 95 %CI:0.35–0.96), and people who smoke vs. those who don’t smoke (aOR = 0.41, 95 %CI:0.24–0.70) were less likely to support a law requiring GHWs. Participants with a low vs. higher level of education (aOR = 0.55, 95 %CI:0.32–0.95) were less likely to support a law requiring a Quitline number. Younger (18–39) vs. older individuals (aOR = 0.53, 95 %CI:0.29–0.94), males vs. females (aOR = 0.57, 95 %CI:0.34–0.96), and participants with a low vs. higher level of education (aOR = 0.56, 95 %CI:0.32–0.98) were less likely to support a law requiring cessation information on cigarette packs. Findings suggest that targeted theory-based public health and communication strategies should be developed to increase awareness and support towards policies that would help reduce cigarette smoking among people from low SEP to eliminate tobacco-related health inequities in the US.