We investigate the spin-period evolutions of recycled pulsars in binary accreting systems .
Taking both the accretion induced field decay and spin-up into consideration , we calculate their spin-period evolutions influenced by the initial magnetic-field strengths , initial spin-periods and accretion rates , respectively .
The results indicate that the minimum spin-period ( or maximum spin frequency ) of millisecond pulsar ( MSP ) is independent of the initial conditions and accretion rate when the neutron star ( NS ) accretes \sim > 0.2 M _ { \odot } .
The accretion torque with the fastness parameter and gravitational wave ( GW ) radiation torque may be responsible for the formation of the minimum spin-period ( maximum spin frequency ) .
The fastest spin frequency ( 716 Hz ) of MSP can be inferred to associate with a critical fastness parameter about \omega _ { c } = 0.55 .
Furthermore , the comparisons with the observational data are presented in the field-period ( B - P ) diagram .