Since a high-speed demand for data transmission is required, Digital Subscriber Line (DSL) is a technology that provides a very high-speed digital data transmission using the regular telephone lines as the transmission media.Asymmetric Digital Subscriber Line (ADSL) technology is one of the DSL technologies that provides asymmetric rate, i.e. different transmission rate in downstream and upstream directions that are required by most of the Internet users.ADSL uses Multicarrier Modulation (MCM) to achieve such high-speed transmission. In this thesis, a design and simulation of an ADSL modem are proposed that can be applied for different telephone networks. The proposed design is based on a Multicarrier Modulation (MCM) method that is called Discrete Multitone (DMT) modulation. This DMT system is based on Quadrature Amplitude Modulation (QAM) and Fast Fourier Transform (FFT). Beside the DMT system, an error detection and correction system that uses efficient coding techniques was built in the modem in order to make the receiver able to recover the data correctly after any error that may occur during transmission due to noise and other channel impairments. Two systems are designed and simulated in this work, the first one is for the downstream path of an ADSL modem by which the channel is divided into 256 subchannels and it used 256 carriers, and the second one for the upstream path by which the channel is divided into 32 subchannels and it uses 32 carriers. The interaction (convolution) between the transmitted signal (DMT symbols) and the telephone channel is achieved by simulating the telephone channel as a Finite Impulse Response (FIR) system with an Additive White Gaussian Noise (AWGN) as a noise source. Both systems (downstream and upstream) were tested under different Signal to Noise (SNR) values to evaluate the systems performance. As a result, 6.16 Mb/s was achieved with Bit Error Rate (BER) = 6.807 ×10−6 at SNR= 33.5 dB in the downstream direction, and 687.5 kb/s was achieved with BER=1.326×10−5 at SNR=25 dB in the upstream direction.