For the purpose of realizing a new intelligent system and its simplified VLSI implementation, we propose a new nonvolatile analog memory called 'switched diffusion analog memory with feedback circuit (FBSDAM)'. FBSDAM has linear writing and erasing characteristics. Therefore, FBSDAM is useful for memorizing an analog value exactly. We also propose a new analog content-addressable memory (CAM) which has neural-like learning and discriminating functions which discriminate whether an incoming pattern is an unknown pattern or a stored pattern. We design and fabricate the CAM using FBSDAM by means of the 4 μm double-poly single-metal CMOS process and nonvolatile analog memory technology which are developed by us. The chip size is 3.1 mm × 3.1 mm. We estimate that the CAM is composed of 50 times fewer transistors and requires 70 times fewer calculation steps than a typical digital computer implemented using similar technology.