Though the mechanism of temperature-induced lower critical solution temperature (LCST) in water is clear for the classic homopolymer poly(N-isopropylacrylamide) (PNIPAM), the LCST of other homopolymer or copolymer remains to be understood. In this work, a novel random copolymer poly(2-hydroxyethyl-co-methyl acrylate) (P(HEA-co-MA)) was prepared. The LCST of the copolymer P(HEA-co-MA) can vary from 11 °C to 65 °C by adjusting flexibly the ratio of the two monomers, showing a broad tunable range. The experimental results showed that the balance of hydrogen bond bridge formed by P(HEA-co-MA) in water and the hydrophobic interaction between polymers can cause the LCST transition of P(HEA-co-MA). An interesting observation is that the sharp phase transition (cosolvency) of P(HEA-co-MA) exists when a rather small amount of alcohol or water is added in polymer solutions at constant temperatures. Moreover, it was found that the increase of LCST is correlated with the increase of alcohol concentration in the water-rich regime, but the decrease of upper critical solution temperature (UCST) is related to the increase of water concentration in the alcohol-rich regime. This work shed light on the understanding of cosolvency by studying the solution behavior of copolymer P(HEA-co-MA) in mixed solvents, which can be of interest for the design of stimuli-responsive polymer materials by variation in solvent composition.