Abstract: Using the WKBsolutions of incompressible Alfvén waves, it is investigated that the propagation of Alfvén waves in the background solar wind with a helmet-shaped current sheet obtained by a time-dependent, two dimensional MHD numerical simulation. The results show that: (1) With increasing heliospheric distance, the Alfvénic magnetic amplitude b will decay Tepidly. Near the heliospkeric sheet, the more slowly of the decay, so that the amplitude of b is almost equal everywhere at large distances. (2) Within several solar radii, the velocity fluctuations reach rapidly the maximum at all latitudes, and after that begin to decay gradualy with increasing distances. At large distances the amplit U de of u over solar polar is a little larger than near the current sheet. (3) With increasing heliospheric distance, the relative magnetic field b/Bwill rise. Over the solar polar the b/B will increase much more slowly than near the current sheet, but above several solar radii, the values of b/B at all latitudes will no longer increase obviously with increasing distance, that is to say, the evolution of the flutuations will reach the so called "saturations", this result may be an important support for Alfvén wave acceleration of the solar wind. Another important result is that near the heliospheric current sheet, b/B > 1 so that Alfvénic fluctuations will be main maglletic field compositions at large distance regions. (4) Near the heliospheric current sheet, the values of the relative velocity fluctuation u/U are the largest and decrease most repidly, instead u/U varies vety slowly over the polar. Within several solar radii, the u/U at all latitudes rapidly becomes vary small, after that at almost same slope and same value, decreases very slowly with increasing distance. Above results show firstly that the propagation nature of polar Alfvén waves is different to that near the heliospheric current sheet.