  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 $\sim>
0.2\ms$. 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.
