A low-cost attitude determination and control system (ADCS) is proposed for nadir-pointing control. This system comprises three-axis magnetorquers and magnetometers. The aim for developing this system is to establish a nadir-pointing control method using only low-cost spacecraft components for active control. Recently, low-cost and reliable development has become a required for spacecraft development. Generally, star trackers, reaction wheels, and thrusters are used for accurate attitude determination and spacecraft control. They have high reliability but their cost becomes a barrier for low-cost spacecraft realization. Contrarily, ADCS, having only magnetorquers and magnetometers, can be low-cost due to their simple composition. Although the magnetic torque generated by magnetorquers is low, nadir-pointing control with magnetorquers can be performed using optimal control algorithm. A Kalman filter for a gyroless spacecraft is applied for attitude determination with a magnetometer. These systems are combined and can realize the pointing accuracy against nadir direction as well as gravity gradient stabilization. Theoretically, spacecraft attitude control with magnetic torque is a well-known singularity problem. Herein, PD control based on an attitude control algorithm, which includes a Singularity Robust (SR) inverse matrix, is proposed as a solution. A PD controller calculates the control torque against attitude error and then an SR inverse matrix is used for computing output magnetic moment. The role of SR inverse matrix is to avoid singularity of the pseudoinverse matrix. Optimal magnetic moment is given by measured magnetic-field value and reference control torque. This study considered two different types of magnetorquers: one with fixed output current and another with variable current. The maximum output is defined with an assumption that this system is used for microsatellites. A fixed output magnetorquer is controlled by a method that is similar to pulse-width modulation to generate desired torque. In the variable model, magnetorquer output is limited by maximum magnetic moment. This paper describes results of nadir-pointing control using both models. Meanwhile, magnetometer-only attitude estimation theory is used for attitude determination. This method is based on extended Kalman-filter estimation. Attitude quaternion and angular velocity are continuously estimated. Although magnetometer-only attitude estimation requires a long conversion time, this method is advantageous for estimating attitude without star trackers, regardless of day and night. Simulations are conducted on various initial attitude and orbital conditions to denote the effectiveness of this method for various Earth-observation satellites such as the Sun-synchronous and International Space Station orbits. Simulation results illustrate that attitude control error can be below 5 deg with both fixed and variable output magnetorquers. It is considered that this control system could be used for active control alternative to gravity gradient stability and backup-control system in high precision attitude control system using star trackers, reaction wheels, and thrusters.