The temperature dependence of the electrical conductivity of the newly developed highly conducting polyacetylene, down to 60 mK, and its high field magnetoconductance up to 15 T are presented. The observed positive magnetoconductance for the most conducting sample exceeds by far the value based on the weak localization theory. The low temperature transport properties vary drastically with small change in the room-temperature conductivity, suggesting that the metallic conduction is realized in the scheme close to metal-nonmetal boundary.