Recently, due to their abundant benefits, current-mode instrumentation amplifiers have received considerable attention in medical instrumentation and read-out circuit for biosensors. This paper is focused on the design of current-mode instrumentation amplifiers for portable, implantable, and wearable electrocardiography and electroencephalography applications. To this end, a CMOS differential voltage second-generation current conveyor (DVCCII) based on a linear transconductor is presented. A new band-pass instrumentation amplifier, based on the designed DVCCII, is also implemented in this paper. The concept of the proposed differential voltage current conveyor and instrumentation amplifier is validated numerically and their predicted performance is presented. The simulation results of the presented circuits were tested for 0.18 μm TSMC CMOS technology in a post layout simulation level using the Cadence Virtuoso tool with a ±0.9 V power supply, and demonstrated that the designed DVCCII has a wide dynamic range of ±400 mV and ±0.85 mA and a power consumption of 148 μW. The layout of the DVCCII circuit occupies a total area of 0.378 μm2. It is shown that the designed DVCCII benefits from good linearity over a wide range of input signals and provides a low input impedance at terminal X. Two versions of the proposed band-pass instrumentation amplifier using pseudo resistances were designed with different specifications for two different applications, namely for EEG and ECG signals. Numerical analyses of both designs show proper outputs and frequency responses by eliminating the undesired artifact and DC component of the EEG and ECG input signals.