In this study, Gaussian white noise and color noise of speech signal are reduced by using adaptive filter and soft computing algorithms. Since the main target is noise reduction of speech signal in a car, ambient noise recorded in a BMW750i is used as color noise in the applications. Signal Noise Ratios (SNR) are selected as +5, 0 and -5 dB for white and color noise. Normalized Least Mean Square (NLMS), Recursive Least Square (RLS) and Genetic Algorithms (GA), Multilayer Perceptron Artificial Neural Network (MLP ANN), Adaptive Neuro-Fuzzy Inference System (ANFIS) are used as adaptive filter and soft computing algorithms, respectively. 5 female and 5 male speakers have been chosen as Speech data from database of Center for Spoken Language Understanding (CSLU) Speaker Verification version 1.1. Noise cancellation performances of the algorithms have been compared by means of Mean Squared Error (MSE). Also processing durations (second) of the algorithms are determined for evaluating possibility of real time implementation. While, the best result is obtained by GA for noise cancellation performance, RLS is the fastest algorithm for real time implementation.