Walsh et al. (1979, Nature, 279, 381) have discovered a double quasar 0957+561, which is of considerable interest. The red magnitudes of the two components, A and B, are identical, being 17, while the blue magnitudes are slightly different. The two components are separated by 5.7 arcsec. The emission spectra of both are extremely similar. Radio observations of 0957+561 have been carried out by Roberts et al. (1979, Science, 205, 894; Bull.Am.Astron.Soc., 11, 620), and by Pooley et al. (1979, Nature, 280, 461). We have proposed a theory of quasars (Varshni, 1973, 1974a, 1974b, 1975, 1977, 1979 and 1985) based on sound physical principles and here we shall estimate the distance of 0957+561 on its basis. Both the components belong to the same group, namely 20, in our spectral classification of quasars. The most natural explanation of the existing observations is that 0957+561 is a binary star embedded in a nebulosity which gives rise to the common absorption lines. We shall draw upon the data for known stars for estimating the distance of 0957+561. From Eggen's compilation (1956, Astron.J. 61, 405) we have selected such binaries which satisfy the following conditions: 1. Spectral types of both components are separately known. 2.Differences between the magnitudes is less than two. Twenty-nine binaries satisfying these conditions were found. In most cases, the spectral types of the two components are quite close; indeed, for seven of them, the spectral types are identical. The similarity with the case 0957+561 is obvious. From a histogram of the number of binaries versus rho/pi (rho=angular separation, pi=trigonometric parallax), it is seen that a great majority (75 percent) of the systems under consideration have rho/pi less than 500 arcsec pc. If we assume that 0957+561 falls in this class, its distance is estimated to be less than 100 pc. The largest value of rho/pi in our list is about 1500 arcsec pc; corresponding to this value, the distance estimate for 0957+561 is 300 pc.