Free-spectral-range (FSR)-free optical filters have always been a critical challenge for photonic integrated circuits. A high-performance FSR-free filter is highly desired for communication, spectroscopy, and sensing applications. Despite significant progress in integrated optical filters, the FSR-free filter with a tunable narrow-band, high out-of-band rejection, and large fabrication tolerance has rarely been demonstrated. In this paper, we propose an exact and robust design method for add-drop filters (ADFs) with an FSR-free operation capability, a sub-nanometer optical bandwidth, and a high out-of-band rejection (OBR) ratio. The achieved filter has a 3-dB bandwidth of < 0.5 nm and an OBR ratio of 21.5 dB within a large waveband of 220 nm, which to the best of our knowledge, is the largest-FSR ADF demonstrated on a silicon photonic platform. The filter exhibits large tunability of 12.3 nm with a heating efficiency of 97 pm/mW and maintains the FSR-free feature in the whole tuning process. In addition, we fabricated a series of ADFs with different periods, which all showed reliable and excellent performances.