In many applications, a constant thrust of the solid propellant rocket motor (SPRM) throughout the operating time is desired. Such thrust-time scenario is known as neutral burning. Typically, tubular grains with internal burning surface yield a progressive thrust-time history and, therefore, if a neutral thrust-time history is required, the progression in the burning surface should be compensated by including the side faces as well. However, neutrality of tubular grain that burns at both of the internal and end surfaces is subject to a limited range of slenderness ratio. Tapering the port at the end faces of the tubular grain would expand the range of the slenderness ratio that ensures neutrality. In the present paper, the issue of neutrality of taper-ended tubular grain is explored. For the studied case, it was found that with normal-ended tube grains neutrality can be realized for slenderness ratio 1.8 and web-to-radius ratio 0.4. However, keeping the same web-to-radius ratio and tapering the ends at angle 25 would slightly worsen the volumetric filling coefficient ( 15% less), but burning neutrality could be attained for slenderness ratios as high as 2.54 ( 40% higher). With this practice, it is possible to maintain neutrality where much longer grains may be adopted for certain applications.