The widespread dissemination of negative information on vaccine may arise people's concern on the safety of vaccine and increase their hesitancy in vaccination, which can seriously impede the progress of epidemic control. Existing works on information-epidemic coupled dynamics focus on the suppression effects of information on epidemic. Here we propose a negative information and epidemic coupled propagation model on two-layer multiplex networks to study the effects of negative information of vaccination on epidemic spreading, where the negative information propagates on the virtual communication layer and the disease spreads on the physical contact layer. In our model, an individual getting an adverse event after vaccination will spread negative information and an individual affected by the negative information will reduce his/her willingness to get vaccinated and spread the negative information. By using the microscopic Markov chain method, we analytically predict the epidemic threshold and final infection density, which agree well with simulation results. We find that the spread of negative information leads to a lower epidemic outbreak threshold and a higher final infection density. However, the individuals' vaccination activities, but not the negative information spreading, has a leading impact on epidemic spreading. Only when the individuals obviously reduce their vaccination willingness due to negative information, the negative information can impact the epidemic spreading significantly.