An electrolyte whose battery capacity, cycle characteristics, load characteristics, and low temperature characteristics are all excellent, and a battery using it. A cathode and an anode are layered and wound with a separator and electrolyte layer in between. The electrolyte layer contains an electrolytic solution containing at least one from the group consisting of vinylethylene carbonate and its derivatives in the range of 0.05 wt % to 5 wt % in total and a polymer. Therefore, chemical stability of the electrolyte layer is improved. It is preferable that the electrolytic solution further contains ethylene carbonate and propylene carbonate with a mass ratio of ethylene carbonate to propylene carbonate ranging from about 15/85 to about 75/25.