This paper presents a wide band, fine-resolution digitally controlled oscillator (DCO) with an on-chip 3-D solenoid inductor using the 0.13 ${mu}m$ digital CMOS process. The on-chip solenoid inductor is vertically constructed by using Metal and Via layers with a horizontal scalability. Compared to a spiral inductor, it has the advantage of occupying a small area and this is due to its 3-D structure. To control the frequency of the DCO, active capacitor and active inductor are tuned digitally. To cover the wide tuning range, a three-step coarse tuning scheme is used. In addition, the DCO gain needs to be calibrated digitally to compensate for gain variations. The DCO with solenoid inductor is fabricated in 0.13 ${mu}m$ process and the die area of the solenoid inductor is 0.013 $mm^2$. The DCO tuning range is about 54 % at 4.1 GHz, and the power consumption is 6.6 mW from a 1.2 V supply voltage. An effective frequency resolution is 0.14 kHz. The measured phase noise of the DCO output at 5.195 GHz is -110.61 dBc/Hz at 1 MHz offset.