An air filtering apparatus using at least three layers of air-permeable mesh structure is disclosed where at least one layer of air-filtering mesh structure contains an anti-bacterial composite material, and at least one layer of air-permeable mesh structure contains material for absorbing airborne non-microbial particles. The combination of three-layer air-permeable mesh structure is effective against airborne microbial matters and volatile organic compounds. A face mask employing such 3-layer air-permeable fabric is also introduced and can be used for effective protection for a prolonged period of time.